an electron is bound in 1D infinite well of width (1x10^-10)m . find the energy values in the ground state and first 2 excited state
Question
An electron is bound in a 1D infinite well of width (1x10^-10)m. Find the energy values in the ground state and first 2 excited states.
Solution
The energy levels of an electron in a 1D infinite potential well (also known as a particle in a box) can be calculated using the formula:
E_n = n²h² / 8mL²
where:
- E_n is the energy of the level n
- n is the quantum number (n=1 for the ground state, n=2 for the first excited state, n=3 for the second excited state, etc.)
- h is the reduced Planck's constant (h = 6.62607015 × 10^-34 m² kg / s)
- m is the mass of the electron (m = 9.10938356 × 10^-31 kilograms)
- L is the width of the well
Let's calculate the energy for the ground state (n=1) and the first two excited states (n=2 and n=3).
- Ground state (n=1):
E_1 = 1² * (6.62607015 × 10^-34 m² kg / s)² / 8 * (9.10938356 × 10^-31 kilograms) * (1x10^-10 m)² E_1 = 6.0246836994 x 10^-19 Joules
- First excited state (n=2):
E_2 = 2² * (6.62607015 × 10^-34 m² kg / s)² / 8 * (9.10938356 × 10^-31 kilograms) * (1x10^-10 m)² E_2 = 2.40987347976 x 10^-18 Joules
- Second excited state (n=3):
E_3 = 3² * (6.62607015 × 10^-34 m² kg / s)² / 8 * (9.10938356 × 10^-31 kilograms) * (1x10^-10 m)² E_3 = 5.4222168292 x 10^-18 Joules
So, the energy of the ground state is approximately 6.02 x 10^-19 Joules, the energy of the first excited state is approximately 2.41 x 10^-18 Joules, and the energy of the second excited state is approximately 5.42 x 10^-18 Joules.
Similar Questions
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.
A particle is confined in a 1D box (0<x<L). The ratio of the energies of the particle in state n=3 to state n=2 isa.9/4b.1/4c.4
The energy (in eV) required to excite an electron from n=2 to n=4 state in hydrogen atom is−0.85+4.25−3.4+2.55
An electron has a linear momentum of 4.0 × 10-25 kg m s-1 . What is the order of magnitude ofthe kinetic energy of the electron?
How many total electrons can the p orbitals hold?A.10B.2C.3D.6SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.