Lowest enersy of an electroa trapped as a potential well as 38 eV Calculate the
width of the cell-
Answers
Answer:
. Calculate the wavelength associated with an electron with energy 2000 eV.
Sol: E = 2000 eV = 2000 × 1.6 × 10–19 J
images
2. Calculate the velocity and kinetic energy of an electron of wavelength 1.66 × 10 –10 m.
Sol: Wavelength of an electron (λ) = 1.66 × 10–10 m
images
To calculate KE:
images
3. An electron is bound in one-dimensional infinite well of width 1 × 10–10 m. Find the energy values in the ground state and first two excited states.
Sol: Potential well of width (L) = 1 × 10–10 m
images
For ground state n = 1,
E2 = 4E1 = 2.415 × 10−17 J
= 150.95 eV
E3 = 9E1 = 5.434 × 10−17 J
= 339.639 eV.
4. An electron is bound in one-dimensional box of size 4 × 10–10 m. What will be its minimum energy?
Sol: Potential box of size (L) = 4 × 10–10 m
images
5. An electron is moving under a potential field of 15 kV. Calculate the wavelength of the electron waves.
Sol: V = 15 × 103 V λ = ?
images
6. Find the least energy of an electron moving in one-dimensional potential box (infinite height) of width 0.05nm.
images
7. A quantum particle confined to one-dimensional box of width ‘a’ is known to be in its first excited state. Determine the probability of the particle in the central half.
Sol: Width of the box, L = a
First excited state means, n = 2
Probability at the centre of the well, P2 (L/2) = ?
images
The probability of the particle at the centre of the box is zero.
8. An electron is confined in one-dimensional potential well of width 3 × 10–10 m. Find the kinetic energy of electron when it is in the ground state.
Sol: One-dimensional potential well of width, L = 3 × 10–10 m
Electron is present in ground state, so n = 1
E1 = ?
images
images
9. Calculate the de Brogile wavelength of neutron whose kinetic energy is two times the rest mass of electron (given mn = 1.676 × 10–27 kg, me = 9.1 × 10–31 kg, C = 3 × 10 8 m/s and h = 6.63 × 10–34 J.S).
Sol: Kinetic energy of neutron, images
where mn = mass of neutron
me = mass of an electron
de Brogile wavelength of neutron, λn = ?
images