nuclei

Question 1

composition of nucleus

Answer 1

Nucleus consists of protons and neutrons.

Question 2

for a neutral atom

Answer 2

For a neutral atom, Number of proton ( ) Z = Number of electron
this number is called the atomic number.

Question 3

what is mass number

Answer 3

The sum of the number of protons and neutrons is called the mass number A.

Question 4

properties of nucleus

Answer 4

nuclear size
(a)Size of the nucleus is of the order of fermi
(b) The radius of the nucleus is given by R=RoA^1/3
R0 = 1.3 fermi and A is the mass number

Question 5

property of nucleus(volume)

Answer 5

The volume of nucleus is V=4/3 π(Ro A^(1/3) )^3, where, R_0= radius of the nucleus

Question 6

property of nucleus(density)

Answer 6

(a) Density =” Mass of nucleus “ /” Volume of the nucleus “ =(Am_p)/(4/3 π(R_0 A^(1/3) )^3 )=m_p/(4/3 πR_0^3 )
where, m_p=1.6×10^(-27) “ “ kg= mass of proton and R_0=1.3 fermi.
(b) Density of nuclear matter is of the order of 10^17 “ “ kg/m^3.
(c) Density of nuclear matter is independent of the mass number.

Question 7

law of radioactive decay

Answer 7

Mathematically, dN/dt∝N or dN/dt=-λN
Here, λ is a proportionality constant, known as the decay constant (or disintegration constant). Unit of λ is s^(-t) or day ^(-1) or year ^(-1), etc.

Question 8

number of nuclei present after time t is given by

Answer 8

N=N_0 e^-λt

where, N_0= number of nuclei present at time t=0.

Question 9

, number of nuclei decayed in time t will be

Answer 9

├ N-N_0=N_0∣e^(-λt)-1]

= number of daughter nuclei produced at time t.

Question 10

Half-Life Period (T_(1/2) ) It is the time in which, activity of the sample falls to one-half of its initial value. Thus, for t=T/2,N=N_0/2 and R=R_0/2

Answer 10

The half-life period is related to decay constant λ as

T_1/2=0.693/λ

Question 11

After n half-lives, the quantity of a radioactive substance left Intact (undecayed) is given by

Answer 11

N=N_0 (1/2)^n=N_0 (1/2)^(i/T_(1/2) )