Advertisements
Advertisements
Question
A proton and an electron are accelerated by the same potential difference. Let λe and λpdenote the de Broglie wavelengths of the electron and the proton, respectively.
Options
λe = λp
λe < λp
λe > λp
The relation between λe and λp depends on the accelerating potential difference.
Advertisements
Solution
λe > λp
Let me and mp be the masses of electron and proton, respectively.
Let the applied potential difference be V.
Thus, the de-Broglie wavelength of the electron,
`λ_e = h/sqrt(2m_eeV)` ....(1)
And de-Broglie wavelength of the proton,
`λ_p = h/sqrt(2m_peV)` ....(2)
Dividing equation (2) by equation (1), we get :
`λ_p/λ_e = sqrt(m_e)/sqrt(m_p)`
`m_e < m_p`
`therefore λ_p/λ_e < 1`
⇒ `λ_p < λ_e`
APPEARS IN
RELATED QUESTIONS
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)
Plot a graph showing variation of de Broglie wavelength λ versus `1/sqrtV` , where V is accelerating potential for two particles A and B, carrying the same charge but different masses m1, m2 (m1 > m2). Which one of the two represents a particle of smaller mass and why?
A proton and an α-particle are accelerated through the same potential difference. Which one of the two has less kinetic energy? Justify your answer.
An α-particle and a proton are accelerated through the same potential difference. Find the ratio of their de Broglie wavelength.
Calculate the de-Broglie wavelength of an electron moving with one-fifth of the speed of light.Neglect relativistic effects. (`h = 6.63 xx 10^(-34)` J.s, c= `3xx10^8`m/s, mass of electron = `9 xx 10^(-31) kg)`
Show on a graph the variation of the de Broglie wavelength (λ) associated with an electron, with the square root of accelerating potential (V) ?
Let p and E denote the linear momentum and energy of a photon. If the wavelength is decreased,
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.
Gas exerts pressure on the walls of the container because :
A litre of an ideal gas at 27°C is heated at constant pressure to 297°C. The approximate final volume of the gas is?
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to
Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momentum of B to A is:
If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is:
The de- Broglie wave length of an electron moving with a speed of 6.6 × 105 m/s is approximately
The kinetic energy of electron in (electron volt) moving with the velocity of 4 × 106 m/s will be
Number of ejected photo electrons increase with increase
The de-Broglie wavelength (λ) associated with a moving electron having kinetic energy (E) is given by ______.
