Question

Consider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical boxes. Which particle has the longest wavelength when the system is in the ground state?

Answer 1

Answer:

electron

Explanation:

The energy for particle in a box is given by:

$E=\frac{n^2 h^2}{8mL^2}$

for the system in ground state, n =1

Since, the boxes are identical, L is same for all the three particles.

h is Planck's constant.

Since energy is inversely proportional to wavelength, therefore

$\lambda \propto m$

$m_e$

$\Rightarrow \lambda_e$

Thus, electron has the longest wavelength.