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
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.
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 Å, which is of the order of inter-atomic spacing in the lattice) (me = 9.11 × 10−31 kg).
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).
An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λd, then ______.
An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength ______.
The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : `sqrt2`. Then, the ratio of Vp to Vd will be ______.
Matter waves are ______.
