Advertisements
Advertisements
Question
What is the
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
Advertisements
Solution
Kinetic energy of the electron, Ek = 120 eV
Planck’s constant, h = 6.6 × 10−34 Js
Mass of an electron, m = 9.1 × 10−31 kg
Charge on an electron, e = 1.6 × 10−19 C
(a) For the electron, we can write the relation for kinetic energy as:
`"E"_"k" = 1/2"mv"^2`
Where,
v = Speed of the electron
∴ `"v"^2 = sqrt((2"eE"_"k")/"m")`
= `sqrt((2 xx 1.6 xx 10^(-19) xx 120)/(9.1 xx 10^(-31)))`
= `sqrt(42.198 xx 10^12)`
= 6.496 × 106 m/s
Momentum of the electron, p = mv
= 9.1 × 10−31 × 6.496 × 106
= 5.91 × 10−24 kg m s−1
Therefore, the momentum of the electron is 5.91 × 10−24 kg m s−1.
(b) Speed of the electron, v = 6.496 × 106 m/s
(c) De Broglie wavelength of an electron having a momentum p, is given as:
`lambda = "h"/"p"`
= `(6.6 xx 10^(-34))/(5.91 xx 10^(-24))`
= 1.116 × 10−10 m
= 0.112 nm
Therefore, the de Broglie wavelength of the electron is 0.112 nm.
APPEARS IN
RELATED QUESTIONS
Describe the construction of photoelectric cell.
A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.
The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which
(a) an electron, and
(b) a neutron, would have the same de Broglie wavelength.
What is the de Broglie wavelength of a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s?
An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.
Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27°C) and 1 atm pressure, and compare it with the mean separation between two atoms under these conditions.
State any one phenomenon in which moving particles exhibit wave nature.
Show with the help of a labelled graph how their wavelength (λ) varies with their linear momentum (p).
The wavelength of the matter wave is dependent on ______.
An electron (mass m) with an initial velocity `v = v_0hati (v_0 > 0)` is in an electric field `E = - E_0hati `(E0 = constant > 0). It’s de Broglie wavelength at time t is given by ______.
A proton and an α-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths λp and λa related to each other?
An electron of mass me, and a proton of mass mp = 1836 me are moving with the same speed. The ratio of the de Broglie wavelength `lambda_"electron"/lambda_"proton"` will be:
How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.
What are matter waves?
What is another name for matter waves?
In \[\lambda=\frac{h}{mv}\], what do \[m\] and \[v\] represent, respectively?
Rearranging \[p=\frac{h}{\lambda}\] gives which expression?
Why did de Broglie propose an associated wavelength for a moving particle?
