Advertisements
Advertisements
Question
A hydrogen atom in a state having a binding energy of 0.85 eV makes transition to a state with excitation energy 10.2 e.V (a) Identify the quantum numbers n of the upper and the lower energy states involved in the transition. (b) Find the wavelength of the emitted radiation.
Advertisements
Solution
(a) The binding energy of hydrogen is given by
`E = 13.6/(n^2)eV`
For binding energy of 0.85 eV,
`n_2^2 = 13.6/0.85`
`n_2 = 4`
For binding energy of 10.2 eV,
`n_2^2 = 13.6/10.2 = 16`
n2 = 1.15
⇒ n1 = 2
The quantum number of the upper and the lower energy state are 4 and 2, respectively.
(b) Wavelength of the emitted radiation (λ) is given by
`1/lamda = R (1/n_1^2 - 1/n_2^2)`
Here,
R = Rydberg constant
n1 and n2 are quantum numbers.
`therefore 1/lamda = 1.097 xx 10^7 (1/4 - 1/16)`
`rArr lamda = (16)/(1.097xx3xx10^7)`
= 4 .8617 × 10-7
= 487 nm
APPEARS IN
RELATED QUESTIONS
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
What will be the energy corresponding to the first excited state of a hydrogen atom if the potential energy of the atom is taken to be 10 eV when the electron is widely separated from the proton? Can we still write En = E1/n2, or rn = a0 n2?
The minimum orbital angular momentum of the electron in a hydrogen atom is
The radius of the shortest orbit in a one-electron system is 18 pm. It may be
An electron with kinetic energy 5 eV is incident on a hydrogen atom in its ground state. The collision
Find the binding energy of a hydrogen atom in the state n = 2.
A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?
A group of hydrogen atoms are prepared in n = 4 states. List the wavelength that are emitted as the atoms make transitions and return to n = 2 states.
Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in Lyman series. What wavelength does this latter photon correspond to?
Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number n changes by 2. (a) Find the smallest wavelength emitted by hydrogen. (b) List the wavelength emitted by hydrogen in the visible range (380 nm to 780 nm).
A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron with what kinetic energy will the electron be ejected?
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?
A hydrogen atom moving at speed υ collides with another hydrogen atom kept at rest. Find the minimum value of υ for which one of the atoms may get ionized.
The mass of a hydrogen atom = 1.67 × 10−27 kg.
When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.
Consider an excited hydrogen atom in state n moving with a velocity υ(ν<<c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency ν of the emitted radiation. Compare this with the frequency ν0 emitted if the atom were at rest.
A hydrogen atom makes a transition from n = 5 to n = 1 orbit. The wavelength of photon emitted is λ. The wavelength of photon emitted when it makes a transition from n = 5 to n = 2 orbit is ______.
