Question

A particle of mass 2.0 × 10–26 g is in a one dimensional box of length 4.0 nm. the wavelength of the photon emitted when this particles goes from n  3 to n  2 level is (a) 1.11 × 10–5 m (b) 3 × 10–10 m (c) 8.96 × 10–6 m (d) 2.32 × 10–4 m

Answer 1

use formula for energy of a particle in one dimensional box ie
E = (ℏ.ℏ.π.π.n.n)/(2mL.L)
where L is length of one dimensional quantum box
ℏ is reduced plank constant ( h/ 2π)
n is quantum number.

Answer 2

Given :

Particle of mass, $m = 2.0 * 10^{-26} g$ , make transition from $n_1 = 3$ to $n_2 = 2$

To Find :

wavelength($\lambda$) of transition.

Explanation:

mass of $H^+$ = $6.023*10^{-26}$ g

atomic number of given atom = $\frac{6.023}{2} = 3$

hence atomic number Z = 3 , that is $Li^{2+}$ ion.

We have the transition formula,

$\frac{1}{\lambda} = R_{H}*Z^2(\frac{1}{(n_2)^2} - \frac{1}{(n_1)^2} )$

$\frac{1}{\lambda} = (10 973 731.6 m^{-1})*(3^2)*\frac{5}{36}$

$\lambda = \frac{1}{13717164.5} = 7.29*10^{-8} m$

Learn More About Transitions :

https://brainly.in/question/11630255

https://brainly.in/question/1330730

#SPJ3