December 02, 2021, 02:08:02 AM
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### Topic: Estimating the size of a nanoparticle  (Read 1711 times)

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#### JMSTHN

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##### Estimating the size of a nanoparticle
« on: December 05, 2020, 07:31:35 AM »
Hi guys,

I am studying for a MChem Chemistry and have taken on some extra short courses to help with my learning. I am currently mid-way through my nanochemistry short course. Today we were asked to estimate the size of a nanoparticle using a simplified equation, and whilst I have an answer, I know it is too large by a magnitude of 10. I will post the question below:

To synthesise cadmium sulfide CdS nanocrystals in aqueous solution, 1L of 2 mM solution of CdSO4⋅2.5H2O was mixed with 18 mmol of 1-thioglycerol under stirring (200 rpm, 5 min). Unknown amount of ammonium sulfide was rapidly added under ambient conditions. The resulting solution had room temperature photoluminescence centred at 460 nm. Transmission electron microscopy studies revealed the average size of the nanocrystals of 3.8 nm.

Estimate the size of the nanoparticles from their optical properties using the simplified equation below and compare it to the experimental value. Explain any differences observed. Include unit analysis.

EE(QD)=Eg, + (ħ2pi2 / 2mehR2)

I related the wavelength to energy and substituted that into the equation and have got an answer of 72 nm, which is obviously too large. I would really appreciate some help with this one if possible. Many thanks.

EDIT - meh is the effective mass of the electron and hole
R is the radius of the atom

#### Corribus

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##### Re: Estimating the size of a nanoparticle
« Reply #1 on: December 05, 2020, 09:48:07 AM »
Well unless it's some really basic arithmetic error then it's got to be the values you are putting in your equation, so why don't you start by telling us what you used.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### wildfyr

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##### Re: Estimating the size of a nanoparticle
« Reply #2 on: December 05, 2020, 12:31:21 PM »
Write all your units out and carefully make sure they cancel.

#### RonaldKar

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« Reply #3 on: April 28, 2021, 11:46:33 PM »
Hi,

I am using SVD to solve the linear system Ax = b. I have a condition that estimated values x should always be positive. Is there a way to make sure that estimated values of x are alway positive?
What is the better solution to this problem? I can use Non-linear Least square approach but then it has the problem of being stuck in local minimum based on the start value and the speed.

Regards,
Vijay