(a) Calculate the energy and momentum of a ...

CBSE Class 12 Physics 2022 Term 2 Delhi Set 1 Solved Paper

Question : 9 of 12

Marks: +1, -0

(a) Calculate the energy and momentum of a photon in a monochromatic beam of wavelength

331.5\text{ nm}

(b) How fast should a hydrogen atom travel in order to have the same momentum as that of the photon in part (a)?

Solution:

(a) Energy

= E = \frac{hc}{\lambda}

Or,

E = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{331.5 \times 10^{-9}}

\therefore E = 6 \times 10^{-19}\text{ J}

Momentum

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

Or,

p = \frac{6.6 \times 10^{-34}}{331.5 \times 10^{-9}}

\therefore p = 2 \times 10^{-27}\text{ kg.m/s}

(b) Momentum of Hydrogen atom

= p = 2 \times 10^{-27}\text{ kg.m/s}

p = mv

Or,

v = \frac{p}{m}

Or,

v = \frac{2 \times 10^{27}\text{ kg.m/s}}{1\text{ a.m.u.}}

Or,

v = \frac{2 \times 10^{-27}\text{ kg.m/s}}{1.66 \times 10^{-27}\text{ kg}}

\therefore v = 1.2\text{ m/s}

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