Question
The wavelength of a $$1\,keV$$ photon is $$1.24 \times {10^{ - 9}}m.$$ What is the frequency of $$1\,MeV$$ photon?
A.
$$1.24 \times {10^{15}}Hz$$
B.
$$2.4 \times {10^{20}}Hz$$
C.
$$1.24 \times {10^{18}}Hz$$
D.
$$2.4 \times {10^{23}}Hz$$
Answer :
$$2.4 \times {10^{20}}Hz$$
Solution :
Energy of photon is $$E = h\nu = \frac{{hc}}{\lambda }$$
As, $$\frac{{hc}}{\lambda } = {10^3}eV$$
$$\therefore h = \frac{{{{10}^3}\lambda }}{c}\,......\left( {\text{i}} \right)$$
And for 2nd case as given in question
$$h\nu = {10^6}eV\,.......\left( {{\text{ii}}} \right)$$
Putting value of $$h$$ in Eq. (ii),
$$\eqalign{
& \frac{{{{10}^3}\lambda }}{c}\nu = {10^6} \cr
& \therefore \nu = \frac{{{{10}^3}c}}{\lambda } \cr
& = \frac{{{{10}^3} \times 3 \times {{10}^8}}}{{1.24 \times {{10}^{ - 9}}}}\,\,\left[ {\because \lambda = 1.24 \times {{10}^{ - 9}}m} \right] \cr
& = 2.4 \times {10^{20}}Hz \cr} $$