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Question

A photon of 400 nm is absorbed by a gas molecule and then the molecule re-emits two photons. One re-emitted photon has wavelength 500 nm. Assuming that there is no change in the energy of molecules, the wavelength of second re-emitted photon is:

A
100 nm
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B
2000 nm
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C
1000 nm
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D
1500 nm
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Solution

The correct option is B 2000 nm
E=E1+E2
where E1 and E2 is the Energy of photon 1 and photon 2 and E=hcλ
hcλ=hcλ1+hcλ2
or 1λ=1λ1+1λ2

1400=1500+1λ2
On solving,
λ2=2000 nm

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