Question 16: Dual Nature of Matter and Radiation

Question

The velocity of an electron so that its momentum is equal to that of a photon of wavelength $$660 \mathrm{~nm}$$ is

Accepted Answer

To find the velocity of the electron such that its momentum is equal to that of a photon with a wavelength of $$660 \, \mathrm{nm}$$, we can follow these steps:
Step 1: Calculate the momentum of the photon
The momentum $ p $ of a photon is given by:
$$  p = \frac{h}{\lambda}  $$
where:
$ h = 6.626 	imes 10^{-34} \, \mathrm{Js} $ (Planck's constant)
$ \lambda = 660 \, \mathrm{nm} = 660 	imes 10^{-9} \, \mathrm{m} $
Substituting the values:
$$ p = \frac{6.626 	imes 10^{-34}}{660 	imes 10^{-9}} $$
Calculating this gives:
$$ p = 1.004 	imes 10^{-27} \, \mathrm{kg \, m/s} $$
Step 2: Equate the momentum of the electron and calculate its velocity
The momentum of an electron with mass $ m $ and velocity $ v $ is given by:
$$  p = mv  $$
For an electron:
$ m = 9.109 	imes 10^{-31} \, \mathrm{kg} $
Equating the momentum of the electron and photon, we have:
$$ mv = 1.004 	imes 10^{-27} $$
Solving for $ v $ gives:
$$ v = \frac{1.004 	imes 10^{-27}}{9.109 	imes 10^{-31}} $$
Calculating this, we get:
$$ v \approx 1102 \, \mathrm{m/s} $$
Conclusion
The closest option to the calculated velocity is Option B: $ 1098 \, \mathrm{ms}^{-1} $.
Thus, the correct answer is
Option B: $ 1098 \, \mathrm{ms}^{-1} $
.

Answer

$$
109.88 \mathrm{~cm} \mathrm{~s}^{-1}
$$

Answer

$$
1098 \mathrm{~ms} ^{-1}
$$

Answer

$$
1098 \mathrm{~cm} \mathrm{~s}^{-1}
$$

Answer

$$
109 \mathrm{~ms} ^{-1}
$$

Dual Nature of Matter and Radiation

The velocity of an electron so that its momentum is equal to that of a photon of wavelength $660 \mathrm{~nm}$ is

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