What is the semimajor axis (in au) of a planet with an orbital period of 14 years?

5.808 AU

Explanation:

According to Kepler’s Third Law of Planetary motion “The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.  

(1)

Talking in general, this law states a relation between the orbital period of a body (moon, planet, satellite, comet) orbiting a greater body in space with the size of its orbit.  

However, if is measured in years, and is measured in astronomical units (equivalent to the distance between the Sun and the Earth: ), equation (1) becomes:

(2)

Knowing and isolating from (2):

(3)

(4)

Finally:

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.