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
Using Bohr's postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr's radius.
How many electrons in an atom may have the following quantum numbers?
n = 3, l = 0
- Using the Bohr’s model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2 and 3 levels.
- Calculate the orbital period in each of these levels.
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
Using Bohr’s postulates, obtain the expression for total energy of the electron in the nth orbit of hydrogen atom.
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
A filter transmits only the radiation of wavelength greater than 440 nm. Radiation from a hydrogen-discharge tube goes through such a filter and is incident on a metal of work function 2.0 eV. Find the stopping potential which can stop the photoelectrons.
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
The dissociation constant of a weak base (BOH) is 1.8 × 10−5. Its degree of dissociation in 0.001 M solution is ____________.
If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
The angular momentum of electron in nth orbit is given by
When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?
How will the energy of a hydrogen atom change if n increases from 1 to ∞?
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:
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 ______.
State three postulates of Bohr's theory of hydrogen atom.
Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.
