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Dual Nature of Radiation and Matter Ncert Solutions Physics Class 12th Physics Ncert Solutions Class 12th Physics Class 12th Dual Nature of Radiation and Matter

11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10^–10 m?

(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.

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Payal Gupta | Contributor-Level 10

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11.17 De Broglie wavelength of the neutron, $λ$ = 1.40 $\times 10^{- 10}$ m

Mass of neutron, m = 1.66 $\times 10^{- 27}$ kg

Planck’s constant, h = 6.626 $\times 10^{- 34}$ Js

Kinetic energy, $E_{k}$ = $\frac{1}{2} m v^{2}$ ………….(1)

De Broglie wavelength and velocity (v) are related as

$λ = \frac{h}{m v}$ …………….(2)

Combining equation (1) and (2), we get

$E_{k}$ = $\frac{1}{2} m ({\frac{h}{m λ})}^{2}$ = $\frac{h^{2}}{2 m λ^{2}}$ = $\frac{{(6.626 \times 10^{- 34})}^{2}}{2 \times 1.66 \times 10^{- 27} \times ({1.40 \times 10^{- 10})}^{2}}$ = 6.75 $\times 10^{- 21}$ J = $\frac{6.75 \times 10^{- 21}}{1.6 \times 10^{- 19}}$ eV = 42.17 $\times 10^{- 3} e V$

Temperature of the neutron, T = 300 K

Average kinetic energy of the neutron, $E_{k - a v g}$ = $\frac{3}{2} k T$ ,

where k = Boltzmann constant = 1.38 $\times 10^{- 23}$ kg $m^{2} s^{- 2} K^{- 1}$

$E_{k - a v g}$ = $\frac{3}{2} k T$ &n

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11.17 De Broglie wavelength of the neutron, $λ$ = 1.40 $\times 10^{- 10}$ m

Mass of neutron, m = 1.66 $\times 10^{- 27}$ kg

Planck’s constant, h = 6.626 $\times 10^{- 34}$ Js

Kinetic energy, $E_{k}$ = $\frac{1}{2} m v^{2}$ ………….(1)

De Broglie wavelength and velocity (v) are related as

$λ = \frac{h}{m v}$ …………….(2)

Combining equation (1) and (2), we get

Temperature of the neutron, T = 300 K

Average kinetic energy of the neutron, $E_{k - a v g}$ = $\frac{3}{2} k T$ ,

where k = Boltzmann constant = 1.38 $\times 10^{- 23}$ kg $m^{2} s^{- 2} K^{- 1}$

$E_{k - a v g}$ = $\frac{3}{2} k T$ = $\frac{3}{2} \times 1.38 \times 10^{- 23} \times 300 = 6.21 \times 10^{- 21}$ J

The relationship of De Broglie wavelength is given as:

$λ = \frac{h}{\sqrt{2 \times E_{k - a v g} \times m}}$ = $\frac{6.626 \times 10^{- 34}}{\sqrt{2 \times 6.21 \times 10^{- 21} \times 1.66 \times 10^{- 27}}}$ = 1.46 $\times 10^{- 10}$ m = 0.146 nm

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11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10^–10 m?

(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.

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11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10–10 m? (b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.

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11.17 (a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10^–10 m?

(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) k T at 300 K.