Question

An electron and a photon each have the same de-Broglie wavelength of 1.0 nm. The ratio of their linear momenta is

• A. 1:1
• B. 1:2
• C. 2:1
• D. 4:9

Hint:

Both use p = h/wavelength, so equal wavelength gives equal momentum.

Answer 1

The Correct Option is A

Step 1: Start From p = h/lambda:
Since $p = h/\lambda$ holds for both matter waves and photons, momentum is fixed by wavelength alone.

Step 2: Put in Numbers:
Take $h = 6.63 \times 10^{-34}$ J s and $\lambda = 1.0 \times 10^{-9}$ m. Then the momentum of each is \[ p = \frac{6.63 \times 10^{-34}}{1.0 \times 10^{-9}} = 6.63 \times 10^{-25} \text{ kg m/s} \]

Step 3: Compare:
The electron and the photon both have $6.63 \times 10^{-25}$ kg m/s, so the ratio is exactly 1 to 1.

Step 4: Rule Out Others:
Ratios such as 1:2, 2:1 or 4:9 would need different wavelengths. They do not match, so only option 1 works.

Final Answer:
\[\boxed{1:1}\]