Advertisements
Advertisements
प्रश्न
An alpha particle is accelerated through a potential difference of 100 V. Calculate:
- The speed acquired by the alpha particle, and
- The de-Broglie wavelength is associated with it.
(Take mass of alpha particle = 6.4 × 10−27 kg)
Advertisements
उत्तर
(i) `1/2 "mv"^2` = qV
or, `1/2"mv"^2` = 2e × 100
or, mv2 = 400 eV
or, v = `sqrt((400 "eV")/"m")`
or, v = `sqrt((400 xx 1.6 xx 10^-19)/(6.4 xx 10^-27))`
∴ v = 105 m/s
(ii) de-Broglie wavelength = λ = `"h"/sqrt(2"mqV")`
or, λ = `(6.6 xx 10^-34)/(sqrt(2 xx 6.4 xx 10^-27 xx 2 xx 1.6 xx 10^-19 xx 100))`
∴ λ = 1.03 × 10−12 m
APPEARS IN
संबंधित प्रश्न
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.
Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27°C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.
State any one phenomenon in which moving particles exhibit wave nature.
70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the gas through the same range at constant volume will be (assume R = 2 cal/mol-K).
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?
- λ = 10 nm
- λ = 10–1 nm
- λ = 10–4 nm
- λ = 10–6 nm
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.
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
Matter waves are ______.
The graph which shows the variation of `(1/lambda^2)` and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle):
