ompute the energy difference between the ground state and first excited state for an electron in a one-dimensional rigid box of length 10–8 cm. Given m = 9.1 × 10–31 kg and h = 6.626 × 10–34 J sec

The energy levels of an electron in a one-dimensional box are given by the formula:

E_n = n²h² / 8mL²

where:

• E_n is the energy of the nth level,
• h is Planck's constant,
• m is the mass of the electron,
• L is the length of the box.

The energy difference between the first excited state (n=2) and the ground state (n=1) is:

ΔE = E_2 - E_1

Substituting the formula for E_n into the equation for ΔE gives:

ΔE = (4h² / 8mL²) - (h² / 8mL²) = 3h² / 8mL²

Substituting the given values into the equation for ΔE gives:

ΔE = 3(6.626 × 10–34 J sec)² / 8(9.1 × 10–31 kg)(10–8 cm)² = 3(6.626 × 10–34 J sec)² / 8(9.1 × 10–31 kg)(10–10 m)²

Solving this equation gives the energy difference between the ground state and first excited state for an electron in a one-dimensional rigid box of length 10–8 cm.