Band gap energy from absorption data using the Tauc plot method - 03

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NanoWorld

NanoWorld

5 жыл бұрын

#NanoWorld,
Attention Please: Before watching this video, please must watch this video
• Band gap energy (Tauc ...
UV-Vis absorption spectroscopy is a powerful tool use for the characterization of optical properties of nano-materials. Here in this video, I have calculated the optical band-gap energy of anatase Pure Titanium dioxide (TiO2). If you have any questions or need any help, just comment below.
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Пікірлер: 162
@bahmanramazani1099
@bahmanramazani1099 4 жыл бұрын
I would like to thank you for taking your invaluable time out of your schedule to record this priceless video. I really appreciate it.
@kedhareswarasairampasupule6645
@kedhareswarasairampasupule6645 5 жыл бұрын
Please also do for the Gas sensing and Photodetector measurements also, because it's being a hot topic nowadays. Thank you so much for this video lecture.
@Bolya_jyoti
@Bolya_jyoti Жыл бұрын
thank you so much, I am very grateful to see this, and keep posting.
@khanacademynigeria2779
@khanacademynigeria2779 2 жыл бұрын
Thank you so much, but i have a question pls. I noticed the formula you used for the y-axis of the Tauc plot, you didn't consider the thickness of the material. is thickness not needed to find the absorption coefficient (alpha)?
@wingariumleviosa
@wingariumleviosa 5 жыл бұрын
Thanks alot this video just made my day. Won't need to go seniors again n again.
@nazimabatool6772
@nazimabatool6772 4 жыл бұрын
You are right
@hariniyasasri2282
@hariniyasasri2282 4 жыл бұрын
Thank you very much for uploading this video... Very helpful...
@md.joherulalamchanchal63
@md.joherulalamchanchal63 2 жыл бұрын
Hi, can I use absorbance data from FTIR to calculate band gap?
@rahulkumarsahuresearchscho5541
@rahulkumarsahuresearchscho5541 4 жыл бұрын
U r doing a great job. I need EIS and MOTT SCHOTTKY analysis by using ZSimpWIN software. Please add it. Along with that please try to add characterization of TEM also. Then there won't be any need of going to seniors again and again. Thanking you.
@user-my4xk4uu4l
@user-my4xk4uu4l 4 жыл бұрын
I have TiO2 thin film can I calculate direct energy gap by this method
@henokgirma5406
@henokgirma5406 3 жыл бұрын
A nice and easy way of calculating a bandgap. My question is that can I used it for a powder DRS result?
@momangyusuf
@momangyusuf Жыл бұрын
Very useful video. May I ask question? Here it is: I have absorbance data of my sample. I try to find transmittance by using formula T = 1 - Absorbance. But I found some negative values in the results. What do you think about it? Do you have some advice or tricks for this case? Thanks.
@ranjeevparashar331
@ranjeevparashar331 Жыл бұрын
What is the role of thin film thickness in the Tauc plot?
@AyadMahmoud
@AyadMahmoud 5 жыл бұрын
Well explained video ! Thanks (y)
@nanophysitronics9687
@nanophysitronics9687 2 жыл бұрын
Is there is no need to take the thickness t while calculating absorbance coefficient
@zahidurrahaman428
@zahidurrahaman428 4 жыл бұрын
Very helpful. Thank you. Keep up the good work.
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Thanks, will do!
@ap_sp
@ap_sp 3 жыл бұрын
Thank u gentleman, amazing explanation those who r starting and doing research work in critically, and can u explain about electronic transition using spectrum, which will most helpful for us thank u
@syedashobnam2684
@syedashobnam2684 28 күн бұрын
what point did you pick to draw the straigth line
@dr.meenakshipokhriyal6105
@dr.meenakshipokhriyal6105 4 жыл бұрын
This data is of powder sample or thin film?
@harry-ho9ti
@harry-ho9ti 4 жыл бұрын
The uploaded video is really explained well. Can u please upload for FTIR spectroscopy. It will be helpful for all of us.
@achmadnasyori8667
@achmadnasyori8667 3 жыл бұрын
Hay, Could you tell me about 1240 and 2.303.
@rientepaola
@rientepaola 4 жыл бұрын
Very useful video! thx!
@shreyjain6447
@shreyjain6447 3 жыл бұрын
Hi nice work! Why the square power in the 4th col? Ps: You earned a sub bro! Keep up the good work and thanks!
@kavitayadav8351
@kavitayadav8351 3 жыл бұрын
Kya sirf nano materials ka band gap nikal skte h is method se????
@MuhammadHassan-uu4of
@MuhammadHassan-uu4of 16 күн бұрын
Sir in my data the graph peak is not that much big it's a small peaks and the graph doesn't grow like this how i select the band gap line then ?
@Meinan4370
@Meinan4370 4 жыл бұрын
could you make a video describing how to obtain index of reflection from reflectance spectra?
@annieprincy7313
@annieprincy7313 4 ай бұрын
Thank you so much for this video sir.
@surya8776
@surya8776 2 жыл бұрын
Could you please tell the origin version used here
@tatieleborges
@tatieleborges 3 жыл бұрын
Truly helpful, many thanks!
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Glad it was helpful!
@deepahk9904
@deepahk9904 5 жыл бұрын
useful video.Thank you
@deepahk9904
@deepahk9904 5 жыл бұрын
Thank you for this video. Can u please share, video on absorption edge using absorbance data....
@electronicbrains13
@electronicbrains13 5 жыл бұрын
Very helpful thanks a lot....can u plz answer how to find extinction coefficient from abdorbance data
@user-cu7tu6xm4p
@user-cu7tu6xm4p 5 ай бұрын
Very much informative video
@vignanabharathi3619
@vignanabharathi3619 5 жыл бұрын
Thank you for neat explanation....
@nanoworld6122
@nanoworld6122 5 жыл бұрын
your are welcome.
@renjinikrishnakumar2105
@renjinikrishnakumar2105 5 жыл бұрын
Thank You very Much...
@aidamariadiezsarabia4350
@aidamariadiezsarabia4350 5 жыл бұрын
I would like to know what concentration I am supposed to use for doing the UV-Vis spectra. Very helpful video anyway
@jyotiyadav-fg8rh
@jyotiyadav-fg8rh 3 жыл бұрын
What is last column
@ElizabethHaydon
@ElizabethHaydon 4 жыл бұрын
If I do a single nanowire absorption measurement, is it still possible to use the shown equations? even though I am not using a cuvette? I wonder how to calculate the absorption coefficient of a nanowire from the absorbance spectrum.
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Honestly speaking, I don't think, I'm able to answer your question properly and I don't want to misguide you. Anyway, follow this link and also check the cited references of this proposal, if necessary, www.sns.it/sites/default/files/allegati/2019/06/phd_topic_lyon_0.pdf I read it a few months ago. In this proposal, they discussed and mention the technique of absorption of a single nanoparticle. Maybe, this proposal will help you.
@selcukbirdogan9342
@selcukbirdogan9342 4 жыл бұрын
Thank you so much.
@saraelhakim1685
@saraelhakim1685 5 жыл бұрын
Thanks alot, but i would like to understant when calculating (ahv) why did you raise it to power 2 when setting the F(x)?
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Thanks for comment. here is the answer of your question, please completely watch this video. if still have confusion, then feel free to ask. kzfaq.info/get/bejne/qsipfc10stGopJc.html
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Thanks for comment. here is the answer of your question, please completely watch this video. if still have confusion, then feel free to ask. kzfaq.info/get/bejne/qsipfc10stGopJc.html
@banajadandasena4142
@banajadandasena4142 6 ай бұрын
10.36, you have changed ahv to( ahv)2 directly but it is graph between ahv and hv only, I am in doubt,
@aseelzakar6267
@aseelzakar6267 5 жыл бұрын
Thank you soo much for this helpful video. can you send me this video as a word file, please?
@bachcharhadrane3675
@bachcharhadrane3675 5 жыл бұрын
THANK YOU SO MUCH. But i think you should divide in the thickness of your samples when you calculate the coefficient alpha
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Hello bachchar Hadrane! Thanks for the comment. Why should i divide in the thickness? Can you explain it please.
@bachcharhadrane3675
@bachcharhadrane3675 5 жыл бұрын
@@nanoworld6122 theoretically, the beer lambert law say that I=I(0) exp(-alpha*d) where d is the thickness. so after mathematic reasoning we find : alpha = -log(I/I(0)) * ln(10)/d and -log(I/I(0))= A the absorbance and ln(10)=2.303. that's why we should divide by d the thickness. And pratically, the standard thickness of the most sample tanks used in IR devices is of 1cm . so i didn't know it before writing this comment. so we can do easily what you did.
@anamadheya7323
@anamadheya7323 Жыл бұрын
@@bachcharhadrane3675 hi. what if my sample is powder and not a thin film? how do I consider the thickness then?
@mardanian82
@mardanian82 5 жыл бұрын
Excellent
@shengliu1163
@shengliu1163 2 жыл бұрын
Thank you so much
@tramnguyenphamhuyen1058
@tramnguyenphamhuyen1058 Жыл бұрын
My origin version doesn't have the F(x) column available like yours. Can you guide me how to insert it? Thanks
@vz00260
@vz00260 Жыл бұрын
Same. Can u got F(x) now?
@physicswithmureedjilani2515
@physicswithmureedjilani2515 5 жыл бұрын
thanks a lot .
@user-ty5zq9rh5y
@user-ty5zq9rh5y 3 жыл бұрын
hello,can you give us play Mott-Schotty?
@joseluisxochihuajuan7586
@joseluisxochihuajuan7586 5 жыл бұрын
Very interesting. Some bibliographical reference that you can recommend me
@28ravimpandya89
@28ravimpandya89 5 жыл бұрын
Very usefull
@naru_26_shimpi
@naru_26_shimpi 3 жыл бұрын
Heartly Thanks ❤
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Thank you too
@mohsinrazak7208
@mohsinrazak7208 3 жыл бұрын
thank u mate however i would like to know whether u treat absorbance (a) and absorption coefficient (alpha) the same bcz it seems like for tauc plot ordinate u are using (ahv) instead of (alpha hv).
@nanoworld6122
@nanoworld6122 3 жыл бұрын
No, Absorbance and Absorbance coefficient are two different things. Please watch the video carefully you will understand I'm NOT treating them as same. Thank You
@ndhakal1085
@ndhakal1085 Жыл бұрын
@@nanoworld6122 Yes, these two are different and we can see the same in the video. I am little worried whether it is 'Absorbance coefficient' or 'Absorbtion coefficient'? Thanks.
@meenukhan9892
@meenukhan9892 5 жыл бұрын
can anyone tell me how did they export that graph to another one? please reply soon I'm in need urgently.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Just press "control + C " button in your key board. and "control + V" where you want to past it.
@alishamanoj2676
@alishamanoj2676 4 жыл бұрын
It was helpful. But how do we know that our material has direct or indirect band gap? Is there any way to find out the type of band gap from the raw data?
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Yes, from this method (shown in the video) you can know the nature of your material either it is direct bandgap or indirect bandgap. I'll make another video on it. But at the moment, if you are facing difficulties than send me your data at fascinatingNanoWorld@gmail.com, I will help you. Thank you.
@ZaidLHadi
@ZaidLHadi 5 жыл бұрын
thank a lot
@saraj1159
@saraj1159 3 жыл бұрын
thanks so so much!! does the concentration effect the band gap? sorry if the question is funny :/ Also, how about if we have more than one curve.is the band gap will show different peaks, should we consider the first? . Thanks
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Yes, only If the concentration is too low or too high. In these causes, the material will not obey the Beer lambert's law and as a result will give you wrong value of the bandgap energy. You have to consider the maximum absorbance band, the other lower absorbance band at higher wavelength might be due to trapped states in between conduction band valance band.
@jamalaleasabbas5250
@jamalaleasabbas5250 4 жыл бұрын
Thanks a lot for nice video
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Most welcome
@mdshifatussami8350
@mdshifatussami8350 5 жыл бұрын
Thanks for making the video. I have a question. Why did you just draw a tangent by hand instead of making origin do it for you using numerical extrapolation? The way you did it was wrong my friend.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Thanks for comment.
@mnebi
@mnebi 5 жыл бұрын
Very usefull video thank you but i have few questions. Is this graphic for anatase or brookite? Its known that anatase TiO2 has indirect band gap. Than we have to use 1/2 for square in formulations. Am i wrong and the other question can we use tauc plot for indirect band gap graphics thank you.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Hello mnebi! The data which i used in this video is Anatase phase of TiO2. Yes, you are right, Tauc Plot could be used for estimation of direct as well as indirect band-gape energy. All you need is to use square for direct band-gap and 1/2 for indirect in this formulation. Yes, Anatase is indirect band-gap semiconductor. But in some research paper, It is also reported that Anatse TiO2 showed direct band-gap behavior. Our synthesized Anatase TiO2 is direct band-gap. As we plotted it for both direct and indirect, what we find is the curve didn't fit for Indirect band-gap value, however it is fit very well for direct band-gap energy.
@mnebi
@mnebi 5 жыл бұрын
@@nanoworld6122 Thank you for enlightening information. I'il look forward to your new videos.
@shaimbox8552
@shaimbox8552 4 жыл бұрын
How can i create those two columns (absorbance and wavelengths) ? Please help .
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Do you have your data?
@shaimbox8552
@shaimbox8552 4 жыл бұрын
@@nanoworld6122 Thanks for the reply . I don't have the data . How can i acquire data for ZnMgO ?
@mutyasrinivasprasad8777
@mutyasrinivasprasad8777 3 жыл бұрын
can the same method be used for glass samples also
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Yes you can!
@rekharajput7076
@rekharajput7076 3 жыл бұрын
Can you please tell me how to plot bandgap every spectra of multiple result in one graph like for series of sample..
@nanoworld6122
@nanoworld6122 3 жыл бұрын
I will upload a video on it Thank You
@Zim-en7oy
@Zim-en7oy 5 жыл бұрын
Could u enlight me, what is the value of column C(X2) in F(x) row? Thanks. Very useful video.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
In C(X2) column, I put energy conversion formula in F(X). F(X) = 1240 divide by wavelength (column). here is a detailed video on this. kzfaq.info/get/bejne/qsipfc10stGopJc.html
@Zim-en7oy
@Zim-en7oy 5 жыл бұрын
@@nanoworld6122 thx 4 ur response.
@anupradhan7326
@anupradhan7326 5 жыл бұрын
hi nanoworld this video helped me a lot can u please do a tutorial on how to determine the phases of xrd or how to analyse xrd data i am a begineer and having problem with it
@zoraizinfopoint3358
@zoraizinfopoint3358 Жыл бұрын
samw question i have
@ashisborah19921
@ashisborah19921 3 жыл бұрын
How to convert absorbance spectrum to CIELab values? If anyone know, please suggest me any link to a detailed method
@renungreningtyas3823
@renungreningtyas3823 3 жыл бұрын
formula CIELab is from tristimulus values (X Y Z), you can read "AATCC Evaluation Procedure 6-2008" , while XYZ is a function of reflectance, ( I dont know the detail but you can read "ASTM E308" and small information in "A New Method for Computing Optimum Weights for Calculating CIE Tristimulus Values"
@engineeringnetronics..8923
@engineeringnetronics..8923 3 жыл бұрын
please tell me how u are calculate the alpha without knowing the thickness of the sample.
@nanoworld6122
@nanoworld6122 3 жыл бұрын
watch this video kzfaq.info/get/bejne/qsipfc10stGopJc.html here is the answer of your question
@gueraouiamal3579
@gueraouiamal3579 2 жыл бұрын
Tank you plais can u explain mor touc équation
@shyreenification
@shyreenification 5 жыл бұрын
why you multiply 2.303 in the last column
@nanoworld6122
@nanoworld6122 5 жыл бұрын
you must consider watching this video kzfaq.info/get/bejne/qsipfc10stGopJc.html
@bhakya1998
@bhakya1998 2 жыл бұрын
Sir how to find those absorbance and wavelength values?
@pirismail9201
@pirismail9201 Жыл бұрын
by UV-vis
@rosaindica4365
@rosaindica4365 5 жыл бұрын
From where did the value 2.303 came? Kindly elucidate.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Hello Rosa indica! You must watch this video. kzfaq.info/get/bejne/qsipfc10stGopJc.html
@ndhakal1085
@ndhakal1085 Жыл бұрын
So nice to find the useful video. My issue at this point is: I do have transmittance data, how to find the band gap? Condition is I do not have thinness of the film too. Is it possible to solve this problem?
@user-fz1qu3zy4o
@user-fz1qu3zy4o Жыл бұрын
No you need the thickness of the film, you'll calculate alpha=1/d Ln(1/T)
@user-fz1qu3zy4o
@user-fz1qu3zy4o Жыл бұрын
and same steps you'll draw alpha ×h×u = f(hu)
@Cena_4u
@Cena_4u 4 жыл бұрын
Nice
@shobanamohanasundaram6215
@shobanamohanasundaram6215 3 жыл бұрын
For a powder sample, how to find Eg value using tauc method?
@nanoworld6122
@nanoworld6122 3 жыл бұрын
You can calculate it using Kubelka-Munk function
@shobanamohanasundaram6215
@shobanamohanasundaram6215 3 жыл бұрын
@@nanoworld6122 thank you
@MuhammadHassan-uu4of
@MuhammadHassan-uu4of 16 күн бұрын
My graph didn't grow up like this in proper order 😭😭😭 what i have to do sir please guide me 😭😭😭
@vinojayapal2884
@vinojayapal2884 3 жыл бұрын
2.303.is wat value please replay. It is for powder sample
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Watch this video kzfaq.info/get/bejne/qsipfc10stGopJc.html
@matheusmoraesbiondo5708
@matheusmoraesbiondo5708 5 жыл бұрын
Great video! Could you show the reference for this method?
@nanoworld6122
@nanoworld6122 5 жыл бұрын
This method is widely used for UV-Vis Absorption spectroscopy, here is a reference for this method. doi.org/10.1007/s10854-018-9670-3
@kaydee3691
@kaydee3691 4 жыл бұрын
Thanks so much
@nanoworld6122
@nanoworld6122 4 жыл бұрын
You're welcome!
@marcoserra4111
@marcoserra4111 4 жыл бұрын
Hi thankyou, why 2.303?
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Hello, watch this video, kzfaq.info/get/bejne/qsipfc10stGopJc.html
@sonamverma7963
@sonamverma7963 3 жыл бұрын
is this Kubelka-Munk plot??
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Kubelka-Munk Vidoe is there, kzfaq.info/get/bejne/iN9pfcebys6WXYU.html
@ekashmirathore3046
@ekashmirathore3046 3 жыл бұрын
start at 5.45 to see the tauc plot
@aishaaziz9248
@aishaaziz9248 5 жыл бұрын
can you plz make video on how to determine rate constant of dye degradation on origin from lnC/Co vs time please please
@victorruiz4331
@victorruiz4331 5 жыл бұрын
I need it also, do you know hot? can you xplain me please?
@aishaaziz9248
@aishaaziz9248 5 жыл бұрын
@@victorruiz4331 take absorbance spectra of ur sample divide initial absorbance over final of different time period. then take ln of it and plot wrt to time
@victorruiz4331
@victorruiz4331 5 жыл бұрын
Aisha khan I thought that the concentration obtained from the calibration curve, then the constant is the slope of Ln co / c. vs time.
@joseluisxochihuajuan7586
@joseluisxochihuajuan7586 5 жыл бұрын
Some biblical reference to quote it in my thesis, please.
@738shani
@738shani 3 жыл бұрын
Thank you Sir, All is good, but please mention that alpha=2.303*A/d where A=absorption and d= path length of cuvette (10 mm or 1cm) OR thin film thickness
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Yes, you are right
@anamadheya7323
@anamadheya7323 Жыл бұрын
hi! does this mean I should consider "d" as path length of cuvette if my sample is a powder and not a thin film?
@dhanyanp666
@dhanyanp666 3 жыл бұрын
Please do a video on photoluminescence spectroscopy
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Noted, Thanks
@redes2012
@redes2012 5 жыл бұрын
When convert the unit of x axis from wavelength to Energy (eV), the values of y axis also need to be converted due to E equals hc/lambda, it's inverse proportion.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
I make the unit conversion accurately. Here is a detail video, you must watch it. kzfaq.info/get/bejne/qsipfc10stGopJc.html
@mitrihabre8635
@mitrihabre8635 4 жыл бұрын
y is the absorbance fraction
@bhakya1998
@bhakya1998 2 жыл бұрын
Anyone tell me where to get those x and y values?
@AliAbbas-bc2jo
@AliAbbas-bc2jo 3 жыл бұрын
this for direct or indirect
@nanoworld6122
@nanoworld6122 3 жыл бұрын
This is for direct
@bestrong6517
@bestrong6517 5 жыл бұрын
is it the same for reflection data?
@nanoworld6122
@nanoworld6122 5 жыл бұрын
No, the method for plotting of DRS ( Diffuse Reflectance Spectroscopy) data is a little bit different.
@bestrong6517
@bestrong6517 5 жыл бұрын
NanoWorld will you please help me ? Video, links,papers anything
@nanoworld6122
@nanoworld6122 5 жыл бұрын
@@bestrong6517 Video for the reflectance spectroscopy will be uploaded soon.
@bestrong6517
@bestrong6517 5 жыл бұрын
NanoWorld Thank you so much ❤️I can’t wait to watch it .
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Here is your demanded video, kzfaq.info/get/bejne/iN9pfcebys6WXYU.html
@adithya4993
@adithya4993 5 жыл бұрын
can u do a video on photoluminescence plot analysis
@nanoworld6122
@nanoworld6122 5 жыл бұрын
i will try to add a video soon.
@ashasumer5395
@ashasumer5395 5 жыл бұрын
@@nanoworld6122 Waiting for that too.
@kavitayadav8351
@kavitayadav8351 3 жыл бұрын
Hello ,thin film ka band gap bhi ese ni nikalna h
@nanoworld6122
@nanoworld6122 3 жыл бұрын
Yes
@kavitayadav8351
@kavitayadav8351 3 жыл бұрын
@@nanoworld6122 isme film ke thikness ki need nhi hogi
@kavitayadav8351
@kavitayadav8351 3 жыл бұрын
@@nanoworld6122 ????
@valentinacarrasco2824
@valentinacarrasco2824 4 жыл бұрын
Hi, I would like to know where or which tangent line I must draw in my graph www.pastepic.xyz/image/tauc-plot.PRif4 in order to obtain the band gap. Thanks in advance!
@nanoworld6122
@nanoworld6122 4 жыл бұрын
The one, which in near 3 eV.
@valentinacarrasco2824
@valentinacarrasco2824 4 жыл бұрын
@@nanoworld6122 thank you for your time and for both videos!
@kevalhadiyal1458
@kevalhadiyal1458 4 жыл бұрын
I think this is not right way to draw line directly and touch to x-axis after plotting tauc plot, first you should choose two points from linear region and then by taking slope you can draw line
@nanoworld6122
@nanoworld6122 4 жыл бұрын
Thanks for the suggestion.
@shabirmahr9496
@shabirmahr9496 5 жыл бұрын
Teasable noise in the background is really unwanted. could u please remove it. Thanks. Anyhow, great job.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Thanks for your suggestion.
@garrytalaroc
@garrytalaroc 5 жыл бұрын
There are a lot of unnecessary things that you have showed. This video coupd be 5 minutes long.
@nanoworld6122
@nanoworld6122 5 жыл бұрын
Thanks for suggestion.
@Zim-en7oy
@Zim-en7oy 5 жыл бұрын
But, it is so helpful for beginners...
@biijoykhomdram9658
@biijoykhomdram9658 2 жыл бұрын
Thank u but ur formula seems wrong. It missed thickness
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