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: Express the given energy in SI units.
Since \(1\ \text{eV} = 1.6\times10^{-19}\ \text{J}\), a \(10\ \text{eV}\) photon has \(E = 1.6\times10^{-18}\ \text{J}\).

Step 2: Find the frequency first.
From \(E = h\nu\) we get \(\nu = E/h\). Putting numbers,
\(\nu = \dfrac{1.6\times10^{-18}}{6.6\times10^{-34}} = 2.42\times10^{15}\ \text{Hz}\).

Step 3: Get the dynamic mass from momentum.
A photon has momentum \(p = E/c\). Its dynamic mass follows from \(p = mc\), so \(m = p/c = E/c^{2}\). Hence
\(m = \dfrac{1.6\times10^{-18}}{(3\times10^{8})^{2}} = \dfrac{1.6\times10^{-18}}{9\times10^{16}} = 1.78\times10^{-35}\ \text{kg}\).

Step 4: State results.
Both come from the same photon energy: the frequency uses \(E=h\nu\) and the dynamic mass uses \(E=mc^{2}\).
\[\boxed{\nu = 2.42\times10^{15}\ \text{Hz}, \qquad m = 1.78\times10^{-35}\ \text{kg}}\]