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Carbon (Z = 6) with mass number 11 decays to boron (Z = 5).
(a) Is it is β+-decay or a β–-decay?
(b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?
A hot gas emits radiation of wavelengths 46nm,82.8nm and 103.5nm only. Assume that the atoms have only two excited states and the difference between consecutive energy levels decreases as energy is increased. Taking the energy of the highest energy state to be zero, find the energies of the ground state and the first excited state.
Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maximillian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.
A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state.
(a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon moving in the same direction as the incident photon. Neglecting the light emitted by the excited hydrogen atoms in the directions of the incident beam. What wavelengths may be observed in the transmitted beam?
(b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (ϕ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms is ground state. Find the maximum value of λ for which
(a) hydrogen atoms may be ionized,
(b) hydrogen atoms may get excited from the ground state to the first excited state and
(c) the excited hydrogen atoms may emit visible light.
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric filed 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?
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it.
(a) Calculate the momentum carried 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.
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.
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 × 1024 kg, mass of the sun = 2.0 × 1030 kg, earth-sun distance =1.5 × 1011 m.
A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr’s quantization rule for angular momentum, calculate
(a) the smallest possible radius of the electron
(b) the radius of the nth orbit and
(c) the minimum possible speed of the electron.
Consider an excited hydrogen atom in state n moving with a velocity v (v << 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 v of the emitted radiation. Compare this with the frequency v0 emitted if the atom were at rest.