Question

The energy of a photon is 10 eV. Determine (i) the dynamic mass of the photon, (ii) the frequency of the photon.
(Given: \( h = 6.6\times10^{-34}\ \text{J s} \), \( c = 3\times10^{8}\ \text{m/s} \), \( 1\ \text{eV} = 1.6\times10^{-19}\ \text{J} \).)

Hint:

Use \( m = E/c^{2} \) for the dynamic mass and \( \nu = E/h \) for the frequency, after converting 10 eV into joules.

Answer 1

Step 1: Convert the energy into joules.
\[ E = 10\ \text{eV} = 10 \times 1.6\times10^{-19}\ \text{J} = 1.6\times10^{-18}\ \text{J} \]

Step 2: Dynamic (relativistic) mass of the photon.
A photon carries energy \( E \), and by mass-energy equivalence its effective (dynamic) mass is
\[ m = \frac{E}{c^{2}} \]
Substituting the values:
\[ m = \frac{1.6\times10^{-18}}{(3\times10^{8})^{2}} = \frac{1.6\times10^{-18}}{9\times10^{16}} \]
\[ m = 1.78\times10^{-35}\ \text{kg} \]

Step 3: Frequency of the photon.
The photon energy is related to its frequency by Planck's relation
\[ E = h\nu \quad\Rightarrow\quad \nu = \frac{E}{h} \]
Substituting the values:
\[ \nu = \frac{1.6\times10^{-18}}{6.6\times10^{-34}} = 2.42\times10^{15}\ \text{Hz} \]

Final answers:
\[\boxed{m = 1.78\times10^{-35}\ \text{kg}, \qquad \nu = 2.42\times10^{15}\ \text{Hz}}\]