`A` near ultra violet photon of wavelength `300nm` is absorbed by a gas and then emitted as two photons. One photons is of red light with wavelength `760nm`. What would be the wave length of the second photon?

Explanation

It may noted that energy of photon which absorbed is emitted as sum of the energy of two photons.
Energy absorbed `hv=(hc)/(lambda)`
According to available information,
`(hc)/(lambda)=(hc)/(lambda_(1))+(hc)/(lambda_(2)),(1)/(lambda)=(1)/(lambda_(1))+(1)/(lambda_(2)),(1)/(lambda_(2))=[(1)/(lambda)-(1)/(lambda_(1))]`
Now, `lambda = 300 nm , lambda_(1)=760nm,lambda_(2)` can be calculated as :
`(1)/(lambda_(2))=[(1)/(300)-(1)/(760)]=(760-300)/(300xx760)(nm^(-1))`
`(1)/(lambda_(2))=(460)/(760xx300)(nm^(-1))`
`lambda_(2)=(760)/(460)(nm)=496nm`