Question

A subatomic particle of mass 10^-18 microgram is in thermal equilibrium with its surrounding at a temperature of 400k. THen the wavelength of this particle will be

Answer 1

Given that,

Mass of particle $m= 10^{-18}\ μg$

Temperature $T=400\ k$

We need to calculate the wavelength of the particle

Using formula of wavelength

$\lambda=\dfrac{h}{\sqrt{3mkT}}$

Where, m = mass of particle

k = boltzmann constant

T = temperature

h = planck constant

Put the value into the formula

$\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{3\times10^{-18}\times10^{-9}\times1.38\times10^{-23}\times400}}$

$\lambda=1.62\times10^{-10}\ \AA$

Hence, The wavelength of the particle is $1.62\times10^{-10}\ \AA$

Answer 2

Explanation:

Given that,

Mass of particle m= 10^{-18}\ μgm=10

−18

μg

Temperature T=400\ kT=400 k

We need to calculate the wavelength of the particle

Using formula of wavelength

\lambda=\dfrac{h}{\sqrt{3mkT}}λ=

3mkT

h

Where, m = mass of particle

k = boltzmann constant

T = temperature

h = planck constant

Put the value into the formula

\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{3\times10^{-18}\times10^{-9}\times1.38\times10^{-23}\times400}}λ=

3×10

−18

×10

−9

×1.38×10

−23

×400

6.63×10

−34

$$\lambda=1.62\times10^{-10}\ \AA$$

Hence, The wavelength of the particle is $$1.62\times10^{-10}\ \AA$$