If the path-length differences between two identical and coherent beams is two wavelengths when they arrive on a screen, will they produce a dark or a bright spot?
a. bright spotb. dark spot

Bright spot

Explanation:

When we have interference between two identical and coherent beams, the conditions for constructive interference (bright spots) and destructive interference (dark spots) are:

- Costructive interference: the path-length differences between the two waves is an integer multiple of the wavelength of the waves:

where the term on the left is the path difference, and is the wavelength

- Destructive interference: the path-length differences between the two waves is an odd multiple of half the wavelength of the waves:

In this problem, the path-length difference is 2 wavelengths: so, it is an integer multiple of the wavelength, therefore the point is a point of constructive inteference (bright spot).

magnitude and direction

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.