In 1924, the French physicist Louis de Broglie resolved the long-standing problem of wave-particle duality in nature by postulating that a free particle has a characteristic wavelength determined by its momentum; that is λ = h/p,
where h is Planck's constant.
Hence, if a particle is a wave, it must have a characteristic dispersion relation. A dispersion relation is simply a representation of a wave's frequency as a function of wavelength, i. e., f(λ). However, most often scientists use angular frequency ω = 2πf and wave number k = 2π/λ instead of frequency and wavelength. By knowing the dispersion relation ω(k), one can find the phase and group velocities of a wave.
Use the dispersion relation to find the group velocity v_group and phase velocity v_phase. Express your answer in terms of velocity v only.

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

the duration of a photographic flash is related to an rc time constant, which is 0.100 μs for a certain camera.

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.