Advertisements
Advertisements
प्रश्न
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
उत्तर
(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
संबंधित प्रश्न
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
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?
In which of the following transitions will the wavelength be minimum?
Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of trincipal quantum number n?
As one considers orbits with higher values of n in a hydrogen atom, the electric potential energy of the atom
A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by
Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)
(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circle
Find the binding energy of a hydrogen atom in the state n = 2.
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
A hydrogen atom in state n = 6 makes two successive transitions and reaches the ground state. In the first transition a photon of 1.13 eV is emitted. (a) Find the energy of the photon emitted in the second transition (b) What is the value of n in the intermediate state?
What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?
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).
The average kinetic energy of molecules in a gas at temperature T is 1.5 kT. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular from at this temperature? Take k = 8.62 × 10−5 eV K−1.
Average lifetime of a hydrogen atom excited to n = 2 state is 10−8 s. Find the number of revolutions made by the electron on the average before it jumps to the ground state.
Show that the ratio of the magnetic dipole moment to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.
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.
