Question

The momentum of a photon associated with a microwave of wavelength 4.00 cm is:

• A. \(1.66 \times 10^{-32}\) kg ms⁻¹
• B. \(1.83 \times 10^{-34}\) kg ms⁻¹
• C. \(2.05 \times 10^{-34}\) kg ms⁻¹
• D. \(1.66 \times 10^{-34}\) kg ms⁻¹

Hint:

Always double-check units in Dual Nature problems; wavelength must be in meters to match the SI units of Planck's constant.

Answer 1

The Correct Option is A

To find the momentum of a photon associated with a microwave of wavelength 4.00 cm, we use the formula for photon momentum:

\(p = \frac{h}{\lambda}\)

where:

• \(p\) is the momentum of the photon
• \(h\) is Planck's constant, approximately \(6.626 \times 10^{-34} \, \text{Js}\)
• \(\lambda\) is the wavelength of the photon, which is given as 4.00 cm or \(0.04 \, \text{m}\)

Substitute the values into the formula:

\(p = \frac{6.626 \times 10^{-34}}{0.04}\)

Now, perform the calculation:

\(p = 1.6565 \times 10^{-32} \, \text{kg ms}^{-1}\)

Rounding this value to match the significant figures of the provided options, we get:

\(p \approx 1.66 \times 10^{-32} \, \text{kg ms}^{-1}\)

Thus, the correct answer is:

• \(1.66 \times 10^{-32} \, \text{kg ms}^{-1}\)

This matches the first option provided, confirming it to be the correct answer.

Hence, the momentum of the photon associated with the given microwave is \(1.66 \times 10^{-32}\) kg ms⁻¹.