Advertisements
Advertisements
Question
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10−27 kg. (c) Find the kinetic energy of recoil of the atom.
Advertisements
Solution
Given:
Wavelength of light emitted by hydrogen, λ = 656.3 nm
Mass of hydrogen atom, m = 1.67 × 10−27 kg
(a) Momentum (P) is given by
P =`h/lamda`
Here,
h = Planck's constant
λ = Wavelength of light
`therefore p = (6.63xx10^-34)/(656.3 xx 10^-9)`
p = 0.01×10-25
p =1 × 10-27 kgm/s
(b) Momentum, p = mv
Here,
m = Mass of hydrogen atom
v = Speed of atom
`therefore 1xx10^-27 = (1.67xx10^-27)xxU`
`rArr v = 1/1.67 = 0.598 = 0.6 m/s`
(c) Kinetic energy (K) of the recoil of the atom is given by
`K = 1/2mv^2`
Here,
m = Mass of the atom
v = Velocity of the atom
`therefore K = 1/2 xx (1.67xx10^-27)xx(0.6)^2 J`
`K = (0.3006xx10^-27)/(1.6xx10^-19)eV`
`K = 1.9 xx 10^-9 ev`
APPEARS IN
RELATED QUESTIONS
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.
if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:
a)`E_k = -E_p"/"2`
b) `E_k = -E_p`
c) `E_k = -2E_p`
d) `E_k = 2E_p`
Using Bohr's postulates, derive the expression for the orbital period of the electron moving in the nth orbit of hydrogen atom ?
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v
Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:
(i) Absorption spectrum of Lyman series.
(ii) The emission spectrum of the Balmer series.
Write postulates of Bohr’s Theory of hydrogen atom.
According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.
The spectral line obtained when an electron jumps from n = 5 to n = 2 level in hydrogen atom belongs to the ____________ series.
The radius of the third Bohr orbit for hydrogen atom is ____________.
In Bohr model of hydrogen atom, which of the following is quantised?
When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
`bar(v) = 109677 1/n_1^2 - 1/n_f^2`
What points of Bohr’s model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ1/λ2, of the photons emitted in this process is ______.
Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to:
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.
The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.
What is meant by ionisation energy?
Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
If a revolving electron emitted radiation continuously, what would equal the frequency of emitted radiation?
