Advertisements
Advertisements
प्रश्न
Find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of `(3/2)` kT at 300 K.
Advertisements
उत्तर
Temperature of the neutron, T = 300 K
Boltzmann constant, k = 1.38 × 10−23 kg m2 s−2 K−1
Average kinetic energy of the neutron:
`"K'" = 3/2 "kT"`
= `3/2 xx 1.38 xx 10^(-23) xx 300`
= 6.21 × 10−21 J
The relation for the de Broglie wavelength is given as:
`lambda"'" = "h"/(sqrt(2"K'""m"_"n"))`
Where
mn = 1.66 × 10−27 Kg
h = 6.6 × 10−34 Js
K' = 6.75 × 10−21 J
∴ `lambda"'" = (6.63 xx 10^(-34))/sqrt(2 xx 6.21 xx 10^(-21) xx 1.66 xx 10^(-27))`
= 1.46 × 10−10 m
= 0.146 nm
Therefore, the de Broglie wavelength of the neutron is 0.146 nm.
APPEARS IN
संबंधित प्रश्न
What is the
(a) momentum,
(b) speed, and
(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.
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.
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.
Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.
When a light wave travels from air to glass ______.
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
The wavelength of the matter wave is dependent on ______.
A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λp to that λα is _______.
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 ______.
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 ______.
Given below are two statements:
Statement - I: Two photons having equal linear momenta have equal wavelengths.
Statement - II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the correct answer from the options given below.
Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?
Which phenomena support the wave model of light?
Which relation gives the de Broglie wavelength of a particle of mass \[m\] moving with speed \[v\]?
In the de Broglie relation, what does \[\lambda\] represent?
Rearranging \[p=\frac{h}{\lambda}\] gives which expression?
How does the de Broglie wavelength depend on momentum?
Which phenomenon does the concept of matter waves help explain?
