Advertisements
Advertisements
प्रश्न
A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of their accelerating potentials
Advertisements
उत्तर
De-broglie wavelength of the particle is given by,
`lambda = "h"/"p" = "h"/"mv" = "h"/sqrt(2"mqV")` ;
where, V= Accelerating potential and v is the speed of the particle.
Given that, the de-broglie wavelength is same for both proton and a-particle.
Charge on α particle = 2c
Mass of α -particle = 4mp
Charge on proton = qp ;
Mass of α -particle = mP
`lambda_a = lambda_P`
`=> "h"/sqrt(2"m"_alpha"q"_alpha"V"_alpha) = "h"/sqrt(2 "m"_"P" "q"_"P" "V"_"P")`
`=> "m"_alpha"q"_alpha"V"_alpha = "m"_"P" "q"_"P" "V"_"P"`
`=> "V"_"P"/"V"_alpha = ("m"_alpha "q"_alpha)/("m"_"P" "q"_"P") = (4 "m"_"P")/"m"_"P" xx (2"q"_"P")/"q"_"P" = 2/1`
2 : 1 is the required ratio of the accelerating potential.
Also,
`lambda_"a" = lambda_"p"`
`=> "h"/("m"_alpha "v"_alpha) = "h"/("m"_"P" "V"_"P")`
`=> "V"_"P"/"V"_alpha = "m"_alpha/"m"_"p" = (4"m"_"p")/"m"_"p" = 4/1`
4 : 1 is the required ratio of the speed of proton to speed of alpha-particle.
APPEARS IN
संबंधित प्रश्न
Calculate the de Broglie wavelength of an electron moving with - of the speed of light in vacuum (Negelct relativistic effect)
(Planck's constant: h = 6.63 x 10-34 Js, Mass of electron : m = 9.11 x 10-28 g)
Describe in brief what is observed when moving electrons are allowed to fall on a thin graphite film and the emergent beam falls on a fluorescent screen.
Answer the following question.
Obtain the expression for the ratio of the de-Broglie wavelengths associated with the electron orbiting in the second and third excited states of the hydrogen atom.
If the kinetic energy of a free electron double, its de-Broglie wavelength changes by the factor ______.
Light of wavelength 2000 Å falls on a metal surface of work function 4.2 eV.
What is the kinetic energy (in eV) of the fastest electrons emitted from the surface?
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to
A solid sphere is in a rolling motion. In rolling motion, a body possesses translational kinetic energy (kt) as well as rotational kinetic energy (kr) simultaneously. The ratio kt : kr for the sphere is:
A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1 m/s so as to have the same K.E. as that of the boy. The original speed of the man will be:
Find the de-Broglie Wavelength for an electron moving at the speed of 5.0 × 106 m/s. (mass of electron is 9.1 × 10-31)
For what k.e of neutron will the associated de-Broglie wavelength be 1.40 × 10-10 m? mass of neutron= 1.675 × 10-27 kg, h = 6.63 × 10-34 J
