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A near U.V. photon of 300 nm is absorbed by a gas and then remitted as two photons. One photon is red with wavelength760 nm. Hence wavelength of the second photon is
$ E - = E_1 + E_2 now E = { hc \over \lambda} $ $ \therefore { 1 \over \lambda } = { 1 \over \lambda_1 } + { 1 \over \lambda_2 } $
The transition in $He^+$ ion that would have the same wave number as the first Lyman line in hydrogen spectrum is
$ \bar \nu = R Z ^2 [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $ $ \bar \nu_H = R [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $ $ \bar \nu_{He} = R Z ^2 [ { 1 \over n ^2 _1 } - { 1 \over n ^2 _f } ]cm ^ {-1} $
The work function of a metal is 4.2 eV. If radiations of $2000 A ^\circ $ fall on the metal then the kinetic energy of the fastest photo electron is
The work function of a metal is the minimum energy required to remove an electron from the metal surface. If the energy of the incident photon (E = hc/λ) is greater than the work function, the excess energy is given to the emitted electron as kinetic energy. Given: Work function = 4.2 eV, λ = 2000 Å = 2000 × 10^-10 m. Kinetic energy of the fastest photoelectron = hc/λ - Work function = (6.63 × 10^-34 × 3 × 10^8) / (2000 × 10^-10) - (4.2 × 1.6 × 10^-19) = 3.2 × 10^-19 J.
The ratio of the radil of the first three Bohr orbit in H atom is
$ r_n = n^2 a_0 i.e. r \alpha n^2 r1 : r2 : r3 = 1^2 : 2^2 : 3^2 = 1 : 4 : 9 $
The momentum of a particle associated with de-Broglie’s wave length of $ 6 A ^\circ $ is
Frequency of matter wave is equal to v = frequency, v = velocity of particle
$ \lambda = { h \over mv } v = \lambda v \therefore \lambda = { v \over \nu } \therefore { v \over \nu } = { h \over mv } \therefore \nu = { mv^2 \over h } = { 2 K.E \over h } ( K.E = { 1 \over 2} mv ^2) $
The mass of one mole of electron is
For the electronic transition from n = 2 to n = 1 which one of the following will produce shortest wave length?
For the transition from n=2 to n=1, the wavelength emitted is inversely proportional to the nuclear charge (Z). The higher the nuclear charge, the shorter the wavelength emitted. Among the given options, Li^(2+) has the highest nuclear charge (Z=3), so it will emit the shortest wavelength for the n=2 to n=1 transition.
The energy required to dislodge electron from excited isolated H atom (IE = 13.6eV) is
Velocity of electron in the first orbit of H-atom is compared to that of velocity of light is approximately
The velocity of an electron in the first orbit (n=1) of a hydrogen atom is approximately 1/137 times the speed of light. This value is known as the fine-structure constant and arises from the relativistic correction to the Bohr model of the hydrogen atom.
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