Find the energy levels of an electron in a box 1 nm wide. Mass of electron is 9.1 × 10–31 kg. Also findthe energy levels of 10 gm marble in a box 10 cm wide.

The energy levels of a particle in a box can be calculated using the formula for a particle in a one-dimensional box:

E = n²h² / 8mL²

where:

• E is the energy of the level,
• n is the quantum number (1, 2, 3, ...),
• h is Planck's constant (6.626 x 10^-34 J.s),
• m is the mass of the particle, and
• L is the width of the box.

1. For an electron in a box 1 nm wide:

Substitute the given values into the formula:

E = n²(6.626 x 10^-34 J.s)² / 8(9.1 x 10^-31 kg)(1 x 10^-9 m)²

Solving this will give the energy levels for the electron in the box.

2. For a 10 gm marble in a box 10 cm wide:

First, convert the mass of the marble to kg (since the SI unit of mass is kg): 10 gm = 0.01 kg

Then, convert the width of the box to m (since the SI unit of length is m): 10 cm = 0.1 m

Substitute these values into the formula:

E = n²(6.626 x 10^-34 J.s)² / 8(0.01 kg)(0.1 m)²

Solving this will give the energy levels for the marble in the box.

Note: The energy levels calculated will be in Joules (J), since this is the SI unit of energy.