Question

The wave number of a photon is \( 10^4 \, cm^{-1} \). What is its energy in joules? Given: \[ h = 6.6 \times 10^{-34} \, Js, \quad c = 3 \times 10^{10} \, cm/s, \quad \tilde{\nu} = 10^4 \, cm^{-1} \]

• A. \( 3 \times 10^{14} h \)
• B. \( 3 \times 10^{-10} h \)
• C. \( 3 \times 10^{10} h \)
• D. \( 3 \times 10^{-14} h \)

Hint:

The energy of a photon is \( E = h c \tilde{\nu} \), where \( \tilde{\nu} \) is the wave number.

Answer 1

The Correct Option is A

The energy of a photon is given by: \[ E = h c \tilde{\nu} \] Substituting the given values: \[ E = (6.6 \times 10^{-34} \, \text{Js}) \times (3 \times 10^{10} \, \text{cm/s}) \times (10^4 \, \text{cm}^{-1}) \] Simplifying: \[ E = 3 \times 10^{14} h \] Thus, the energy of the photon is \( 3 \times 10^{14} h \).