Atoms, Nuclei & Radioactivity Test - 9

More than 99.99% of the mass of any atom is concentrated in its nucleus. If the mass of protons and neutrons (which are in the nucleus of every atom) is approximately one atomic mass unit, then the relative mass of an electron is 0.0005 atomic mass units.

The binding energy is a very short order range force.
So beyond a certain amount of range the force has no influence beyond that. that 's why after
certain number the binding energy per nucleon do not change even if we add more nucleons.

t_{1/2 ​} =24000 yrs
It is stored for 3 half-lives.
Fraction remaining is (1/2 ​)³ =1/8

In nuclear reactors, fission of uranium is carried out by bombarding  a slow moving neutron on uranium which results in emission of 3 more neutrons along with the byproducts  So, cadmium rods are used to absorb extra neutrons in order to achieve controlled chain reaction.

The atomic mass of an element is the average mass of the atoms of an element measured in atomic mass unit (amu, also known as daltons, D). The atomic mass is a weighted average of all of the isotopes of that element, in which the mass of each isotope is multiplied by the abundance of that particular isotope.

Unlike a chemical reaction, a nuclear reaction results in a significant change in mass and an associated change of energy, as described by Einstein ’s equation. Nuclear reactions are accompanied by large changes in energy, which result in detectable changes in mass. The change in mass is related to the change in energy according to Einstein ’s equation: ΔE = (Δm)c2. Large changes in energy are usually reported in kiloelectronvolts or megaelectronvolts (thousands or millions of electronvolts). With the exception of 1H, the experimentally determined mass of an atom is always less than the sum of the masses of the component particles (protons, neutrons, and electrons) by an amount called the mass defect of the nucleus. The energy corresponding to the mass defect is the nuclear binding energy, the amount of energy released when a nucleus forms from its component particles. In nuclear fission, nuclei split into lighter nuclei with an accompanying release of multiple neutrons and large amounts of energy. The critical mass is the minimum mass required to support a self-sustaining nuclear chain reaction. Nuclear fusion is a process in which two light nuclei combine to produce a heavier nucleus plus a great deal of energy.

Half-life of Bi²¹⁰ =5 days
∴k= 0.693/(t1/2) ​=(0.693/5) ​day⁻¹
Using k=(2.303/t)​log (a/a-x)
(where a = a_{0 ​} , (let) ⇒x=7/8 ​a₀ ​, t is time taken in decay and k is rate constant)
We get, t=(2.303 ×5/0.693)log a₀ ​/(1/8)a₀ ​​
= (2.303 ×5/0.693) ​log8=15days
 

Given, 10% of substance decays in 10 days
So, let [A]_o =100, [A]_t =100-10=90
So, K=(2.303/t) log ([A]_o /[A]_t )
K= (2.303/10) log (100/90)
K= (2.303/10) (log10-log9)
K= (2.303/10)91-0.9542)   [log9=0.9542]
K= (2.303/10) x 0.0458 day^-1
So, after 24 days,
t= (2.303/K) log (100/[A]t)
24=2.303x10/2.303x0.0458) log [100/[A]_t ]
log[100/[A]t]=(24x0.0458)/10=0.1099
100/[A]_t =antiog(0.1099)=1.288
So, [A]_t =100/1.288 ≈100/1.3
[A]_t =76.9 ≈77%
The closest answer is 78% which is option A. So the correct answer would be option A
 

Neutron is unstable outside the nucleus.
It 's decaying equation is given below.
0 ​ⁿ¹ ⇒¹₁ ​H+⁰₋₁ e+v

Substance left undecayed, N₀ ​−(3/4)​N₀ ​=(1/4)​N₀ ​
N/N0 ​​=1/4 ​=(1/2 ​)ⁿ
 
∴Number of atoms left undecided, n=2 i.e, in two half-lives
∴t=nT=2 ×4=8 months

Half-life of radioactive sample, i.e., the time in which the number of undecayed nuclei becomes half (T) is 10 s.
Mean life, τ=T/loge ​2=10s/0.693=1.443 ×10=14.43s ≈15s

When neutrons are added to the nucleus of an atom its chemical properties remain unchanged because the atomic number of particles remains the same. But when electron, proton or alpha particles are added, atomic number changes so chemical properties change.