The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass , is [2017]

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Q.
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass $m$ , is [2017]

1 $\frac{h}{\sqrt{3 m k T}}$

2 $\frac{2 h}{\sqrt{3 m k T}}$

3 $\frac{2 h}{\sqrt{m k T}}$

4 $\frac{h}{\sqrt{m k T}}$

Ans.
(1)

Kinetic energy of a neutron in thermal equilibrium with heavy water at a temperature $T$ is given as

$K = \frac{3}{2} k T$ ...(i)

Also momentum $(p)$ is, $p = \sqrt{2 m K}$

From eqn. (i),

$p = \sqrt{2 m \cdot \frac{3}{2} k T} = \sqrt{3 m k T}$

Required de-Broglie wavelength is given as

$λ = \frac{h}{p} = \frac{h}{\sqrt{3 m k T}}$

Solution

Q.
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass $m$ , is [2017]

1 $\frac{h}{\sqrt{3 m k T}}$

2 $\frac{2 h}{\sqrt{3 m k T}}$

3 $\frac{2 h}{\sqrt{m k T}}$

4 $\frac{h}{\sqrt{m k T}}$

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Solution

Q. The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass m, is [2017]

1 h3mkT

2 2h3mkT

3 2hmkT

4 hmkT

Ans. (1) Kinetic energy of a neutron in thermal equilibrium with heavy water at a temperature T is given as K=32kT ...(i) Also momentum (p) is, p=2mK From eqn. (i), p=2m·32kT=3mkT Required de-Broglie wavelength is given as λ=hp=h3mkT

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Q.
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass $m$ , is [2017]

1 $\frac{h}{\sqrt{3 m k T}}$

2 $\frac{2 h}{\sqrt{3 m k T}}$

3 $\frac{2 h}{\sqrt{m k T}}$

4 $\frac{h}{\sqrt{m k T}}$