Advertisements
Advertisements
प्रश्न
What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.
Advertisements
उत्तर
Energy (E) of the nth Bohr orbit of an atom is given by,
`"E"_"n" = (-(2.18xx10^(-18))"Z"^2)/"n"^2`
Where,
Z = atomic number of the atom
Ground state energy = – 2.18 × 10–11 ergs
= - 2.18 × 10–11 × 10–7 J
= - 2.18 × 10–18 J
Energy required to shift the electron from n = 1 to n = 5 is given as:
ΔE = E5 – E1
`= (-(2.18xx10^(-18))(1)^2)/(5)^2 - (-2.18 xx 10^(-18))`
`= (2.18xx10^(-18))[1 - 1/25]`
`= (2.18xx10^(-18))(24/25)`
`= 2.0928 xx 10^(-18)"J"`
Wavelength of emitted light = `"hc"/"E"`
`= ((6.626xx10^(-34))(3xx10^(8)))/(2.0928xx10^(-18))`
`= 9.498 xx 10^(-8) "m"`
APPEARS IN
संबंधित प्रश्न
An electron is orbiting in 5th Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.
State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of Hα line. [Given: Rydberg constant R = 1.03 × 107 m−1]
Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 1015, calculate the energy of the source.
The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is
(A) – 1
(B) 2
(C) 1/2
(D) – 0.5
Using Bohr’s postulates, obtain the expressions for (i) kinetic energy and (ii) potential energy of the electron in stationary state of hydrogen atom.
Draw the energy level diagram showing how the transitions between energy levels result in the appearance of Lymann Series.
Using Bohr’s postulates, obtain the expression for total energy of the electron in the nth orbit of hydrogen atom.
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
Write postulates of Bohr’s Theory of hydrogen atom.
Mention demerits of Bohr’s Atomic model.
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.
According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 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 ______.
In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
