The density of a certain planet varies with radial distance as: rho(r)= rho0(1-αr/r0) where r0= 25.12 x 10^6 m is the radius of the planet, rho0= 3800.0 kg/m^3 is its central density, and α = 0.24. what is the total mass of this planet ?

The total mass of this planet is

Explanation:

Given that,

Radius

Density

Central density

The density of a certain planet varies with radial distance as

We need to calculate the total mass of this planet

Using formula of density

On integrating

Put the value of into the formula

Put the value into the formula

Hence, The total mass of this planet is

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.