1B.9 HW

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1B.9 HW

Postby Veronica_Lubera_2A » Thu Oct 10, 2019 11:19 am

How would you solve this problem?

A lamp rated at 32W (1 W= 1 J/s) emits violet light of wavelength 420nm. How many photons of light can the lamp generate in 2 sec? How many moles of photons are emitted in that time interval?

Junxi Feng 3B
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Re: 1B.9 HW

Postby Junxi Feng 3B » Thu Oct 10, 2019 11:42 am

I think the best way to solve the problem is dimensional analysis. First, multiply the time 2 sec to the 32W, and notice how the units of time cancel out each other, do the calculation and the result is simply 64 J. Now, use the given wavelength of violet light to find out the frequency by using the formula c= frequency * wavelength. Once we get the frequency, we can use the Einstein equation E= hv to find the energy in Joule per photon. Since the unit for E is J/photon, we just need to divide the 64J by the E we just calculate above, which we can see how unit Joule cancel out, and is left only with the number of photon.

To get the number of moles of photons, simply divide the number of photons by 6.022 x 10^23 mol/photon.

Subashni Rajiv 1K
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Re: 1B.9 HW

Postby Subashni Rajiv 1K » Thu Oct 10, 2019 11:59 am

First convert the given wavelength of 420 nm to m (420 x 10^-9) and multiply the given 32 W to joules (32 J/s). Since the problem tell us it's in 2 seconds, multiply the time with the Joules/sec to give 64 total Joules. Now, use the E=hc/lambda equation and substitute 420 x 10^-9 m for lambda. You should get 4.73 x 10^-19 J for 1 photon. That value is the energy of 1 photon and then using a conversion: 64J x 1 photon / 4.73 x 10^-19 J to get 1.4 x 10^20 photons emitted. To convert it into moles, divide the 1.4 x 10^20 photons by 6.022 x 10^23 to get 2.3 x 10^-4 moles.

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