Advertisements
Advertisements
प्रश्न
An electron is accelerated from rest through a potential difference of 100 V. Find:
- the wavelength associated with
- the momentum and
- the velocity required by the electron.
Advertisements
उत्तर
(i) Wavelength = λ = `"h"/sqrt(2 "meV")`
λ = `(6.6 xx 10^-34)/sqrt(2 xx 9.1 xx 10^-31 xx 1.6 xx 10^-19 xx 100)`
= 1.2 × 10−10 m
∴ λ = 1.2 Å
(ii) Momentum = p = `"h"/λ`
p = `(6.6 xx 10^-34)/(1.2 xx 10^-10)`
∴ p = 5.5 × 10−24 kg m/s
(iii) Momentum = p = mv
∴ Velocity = v = `"p"/"m"`
= `(5.5 xx 10^-24)/(9.1 xx 10^-31)`
= 6 × 106 m/s
संबंधित प्रश्न
Calculate the de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
What is the
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E = hv, p = `"h"/lambda`
But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?
A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values λ1, λ2 with λ1 > λ2. Which of the following statement are true?
- The particle could be moving in a circular orbit with origin as centre.
- The particle could be moving in an elliptic orbit with origin as its focus.
- When the de Broglie wavelength is λ1, the particle is nearer the origin than when its value is λ2.
- When the de Broglie wavelength is λ2, the particle is nearer the origin than when its value is λ1.
The De-Broglie wavelength of electron in the third Bohr orbit of hydrogen is ______ × 10-11 m (given radius of first Bohr orbit is 5.3 × 10-11 m):
The equation λ = `1.227/"x"` nm can be used to find the de Brogli wavelength of an electron. In this equation x stands for:
Where,
m = mass of electron
P = momentum of electron
K = Kinetic energy of electron
V = Accelerating potential in volts for electron
A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be:
How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.
