Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Physics

The radionuclide ¹¹C decays according to 

\[\ce{^11_6C -> ^11_5B + e+ + \text{v}}\] : T_1/2 = 20.3 min

The maximum energy of the emitted positron is 0.960 MeV.

Given the mass values: `"m"(""_6^11"C") = 11.011434 u and "m"(""_6^11"B") = 11.009305 "u"`

Calculate Q and compare it with the maximum energy of the positron emitted.

The Q value of a nuclear reaction \[\ce{A + b → C + d}\] is defined by

Q = [ m_A+ m_b− m_C− m_d]c² where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]

Atomic masses are given to be

`"m"(""_1^2"H")` = 2.014102 u

`"m"(""_1^3"H")` = 3.016049 u

`"m"(""_6^12"C")` = 12.000000 u

`"m"(""_10^20"Ne")` = 19.992439 u

The Q value of a nuclear reaction A + b → C + d is defined by

Q = [m_A+ m_b − m_C − m_d]c² where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

\[\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}\]

Atomic masses are given to be

`"m"(""_1^2"H")` = 2.014102 u

`"m"(""_1^3"H")` = 3.016049 u

`"m"(""_6^12C)` = 12.000000 u

`"m"(""_10^20"Ne")` = 19.992439 u

A source contains two phosphorous radio nuclides `""_15^32"P"` (T_{1/2 =} 14.3d) and `""_15^33"P"` (T_1/2 = 25.3d). Initially, 10% of the decays come from `""_15^33"P"`. How long one must wait until 90% do so?

Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes:

\[\ce{^223_88Ra -> ^209_82Pb + ^14_6C}\]

\[\ce{^223_88 Ra -> ^219_86 Rn + ^4_2He}\]

Calculate the Q-values for these decays and determine that both are energetically allowed.

A radioactive nucleus 'A' undergoes a series of decays as given below:

The mass number and atomic number of A₂ are 176 and 71 respectively. Determine the mass and atomic numbers of A₄ and A.

(a) Derive the relation between the decay constant and half life of a radioactive substance. 
(b) A radioactive element reduces to 25% of its initial mass in 1000 years. Find its half life.

Define the capacitance of a capacitor. Obtain the expression for the capacitance of a parallel plate capacitor in vacuum in terms of plate area A and separation d between the plates.

 A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has a thickness \[\frac{3d}{4}\]. Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric. 

Define 'activity' of a radioactive substance ?

Two different radioactive elements with half lives T₁ and T₂ have N₁ and N₂ undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N₁ and N_{2 ?}

Why is it experimentally found difficult to detect neutrinos in this process ?

A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if the refractive index of the material of the sphere is \[\sqrt{3}\].

In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10⁻³m² and the separation between the plates is 3 mm.

1. Calculate the capacitance of the capacitor.
2. If this capacitor is connected to 100 V supply, what would be the charge on each plate?
3. How would charge on the plates be affected, if a 3 mm thick mica sheet of k = 6 is inserted between the plates while the voltage supply remains connected?

Define the activity of a given radioactive substance. Write its S.I. unit.

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor. 

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/3, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness 2d/3, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.

In a given sample, two radioisotopes, A and B, are initially present in the ration of 1 : 4. The half lives of A and B are respectively 100 years and 50 years. Find the time after which the amounts of A and B become equal.

A parallel-plate capacitor is charged to a potential difference V by a dc source. The capacitor is then disconnected from the source. If the distance between the plates is doubled, state with reason how the following change:

(i) electric field between the plates

(ii) capacitance, and

(iii) energy stored in the capacitor