Answer
a) $P_n=\frac{h}{\frac{2L}{n}}$ where $n=1,2,3,.......$
b) $E_n=\frac{n^2h^2}{8mL^2}$ $n=1,2,3,....$
Work Step by Step
(a) We know that
$P_n=\frac{h}{\lambda_n}$
but $\lambda_n=\frac{2L}{n}$
$\implies P_n=\frac{h}{\frac{2L}{n}}$ where $n=1,2,3,.......$
(b) We know that the energy of the particle is given as
$E_n=\frac{P_n^2}{2m}$
$\implies E_n=\frac{n^2h^2}{\frac{4L^2}{2m}}$
$\implies E_n=\frac{n^2h^2}{8mL^2}$ $n=1,2,3,....$
