Question

A particle is moving in a one-dimensional box of width 10 Å. Calculate the probability of finding

the particle within an interval of 2 Å at the centre of the box when it is in the state of least energy

Answer 1

Width of box, $l=10\space A^o$

Interval, $x=2\space A^o$

Since the electron is in its least energy state, $n=1$

Probability function, $\Psi_m=\sqrt{\dfrac{2}{l}}\space sin\bigg(\dfrac{n\pi x}{l}\bigg)$

$\Psi_m=\sqrt{\dfrac{2}{10}}\space sin\bigg(\dfrac{\pi\times 2}{10}\bigg)$

$\Psi_m=0.138$