Question

The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is \(10^{16}\,\text{s}^{-1}\). The wave number of photon 'C' is \(10^{5}\,\text{cm}^{-1}\). The correct order of energy of these photons is:

• A. C>B>A
• B. B>A>C
• C. A>C>B
• D. A>B>C

Hint:

Always convert wavelength, frequency, and wave number into SI units before calculating photon energy.

Answer 1

The Correct Option is A

To determine the correct order of energy for the photons given their respective properties, we need to calculate the energy for each photon using the information provided: wavelength, frequency, and wave number.

1. The energy of a photon is calculated using the formula: \(E = h \nu\), where \(E\) is the energy, \(h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}\) is Planck's constant, and \(\nu\) is the frequency.
2. For Photon A:
   1. Given the wavelength \(\lambda = 400 \, \text{nm} = 400 \times 10^{-9} \, \text{m}\).
   2. The frequency is calculated using: \(\nu = \frac{c}{\lambda}\), where \(c = 3 \times 10^8 \, \text{m/s}\) is the speed of light.
   3. Calculate the frequency: \(\nu = \frac{3 \times 10^8}{400 \times 10^{-9}} = 7.5 \times 10^{14} \, \text{s}^{-1}\)
   4. Substituting in the energy formula: \(E_A = h \cdot \nu = 6.626 \times 10^{-34} \times 7.5 \times 10^{14} = 4.9695 \times 10^{-19} \, \text{J}\)
3. For Photon B:
   1. Given the frequency \(\nu = 10^{16} \, \text{s}^{-1}\).
   2. Calculate energy: \(E_B = h \cdot \nu = 6.626 \times 10^{-34} \times 10^{16} = 6.626 \times 10^{-18} \, \text{J}\)
4. For Photon C:
   1. Given the wave number \(\bar{\nu} = 10^5 \, \text{cm}^{-1}\).
   2. The wave number is related to wavelength by \(\bar{\nu} = \frac{1}{\lambda}\).
   3. Convert wave number to wavelength: \(\lambda = \frac{1}{10^5} \, \text{cm} = 10^{-5} \, \text{cm} = 10^{-7} \, \text{m}\)
   4. Frequency is given by \(\nu = \frac{c}{\lambda} = \frac{3 \times 10^8}{10^{-7}} = 3 \times 10^{15} \, \text{s}^{-1}\)
   5. Calculate energy: \(E_C = h \cdot \nu = 6.626 \times 10^{-34} \times 3 \times 10^{15} = 1.9878 \times 10^{-18} \, \text{J}\)

Now, comparing the energies:

• \(E_C = 1.9878 \times 10^{-18} \, \text{J}\)
• \(E_B = 6.626 \times 10^{-18} \, \text{J}\)
• \(E_A = 4.9695 \times 10^{-19} \, \text{J}\)

Thus, the order of energy of these photons is: C > B > A. Therefore, the correct answer is: C > B > A.