Advertisements
Advertisements
Question
Two particles have the same de Broglie wavelength and one is moving four times as fast as the other. If the slower particle is an α-particle, what are the possibilities for the other particle?
Advertisements
Solution
Data:
λ1 = λ2,
v1 = 4v2
λ = `h/p = h/(mv)`
∴ `lambda_1 = h/(m_1v_1)`,
`lambda_2 = h/(m_2v_2)`
As λ1 = λ2,
m1v1 = m2v2
∴ `m_1 = (m_2 v_2)/v_1 = m_2 (1/4) = m_2/4`
As particle 2 is the ex-particle, particle 1 (having the mass `1/4` times that of the a-particle) may be a proton or neutron.
APPEARS IN
RELATED QUESTIONS
State the importance of Davisson and Germer experiment.
An electron is accelerated through a potential of 120 V. Find its de Broglie wavelength.
The momentum of a photon of energy 1 MeV in kg m/s will be ______
The de Broglie wavelength associated with photon is, ____________.
If the radius of the innermost Bohr orbit is 0.53 Å, the radius of the 4th orbit is ______
According to de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is 'λe'· Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is 'λp'. If the energy (E) of electron and photon is same then relation between 'λe' and 'λp' is ______.
An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is ( c being velocity of light) ______.
If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be (Ei and Ef are the initial and final kinetic energies of the particle respectively.)
A particle of charge q, mass m and energy E has de-Broglie wavelength `lambda.` For a particle of charge 2q, mass 2m and energy 2E, the de-Broglie wavelength is ____________.
How much energy is imparted to an electron so that its de-Broglie wavelength reduces from 10-10 m to 0.5 × 10-10 m? (E =energy of electron)
The wavelength '`lambda`' of a photon and de-Broglie wavelength of an electron have same value. The ratio of energy of a photon to kinetic energy of electron is (m = mass of electron, c = velocity of light, h = Planck's constant) ____________.
If '`lambda_1`' and '`lambda_2`' are de-Broglie wavelengths for electrons in first and second Bohr orbits in hydrogen atom, then the ratio '`lambda_2`' to '`lambda_1`' is (E1 = -13.6 eV) ____________.
If the kinetic energy of a particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is ____________.
If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?
According to de-Broglie hypothesis, the ratio of wavelength of an electron and that of photon having same energy 'E' is (m = mass of electron, c = velocity of light) ____________.
A photon of wavelength 3315 Å falls on a photocathode and an electron of energy 3 x 10-19 J is ejected. The threshold wavelength of photon is [Planck's constant (h) = 6.63 x 10-34 J.s, velocity of light (c) = 3 x 108 m/s] ____________.
Explain de-Broglie wavelength.
Obtain an expression for de-Broglie wavelength of wave associated with material particles. The photoelectric work function for metal is 4.2 eV. Find the threshold wavelength.
An electron of mass m has de-Broglie wavelength λ when accelerated through potential difference V. When proton of mass M, is accelerated through potential difference 9V, the de-Broglie wavelength associated with it will be ______. (Assume that wavelength is determined at low voltage)
An electron is accelerated through a potential difference of 100 volts. Calculate de-Broglie wavelength in nm.
Calculate the de Broglie wavelength associated with an electron moving with a speed of `5 xx 10^6` m/s. `(m_e = 9.1 xx 10^(-31)kg)`
A photon and an electron have an equal energy ‘E’. The ratio of wavelength ‘λp’ of photon to that of electron ‘λe’ is proportional to ______.
If the potential difference used to accelerate electrons is tripled, by what factor does the de-Broglie wavelength associated with electrons change?
