PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Physics

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively

Lithium (Z = 3) has two stable isotopes ⁶Li and ⁷Li. When neutrons are bombarded on lithium sample, electrons and α-particles are ejected. Write down the nuclear process taking place.

The masses of ¹¹C and ¹¹B are respectively 11.0114 u and 11.0093 u. Find the maximum energy a positron can have in the β*-decay of ¹¹C to ¹¹B.

(Use Mass of proton m_p = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_n = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c²,1 u = 931 MeV/c².)

²⁸Th emits an alpha particle to reduce to ²²⁴Ra. Calculate the kinetic energy of the alpha particle emitted in the following decay:

`""^228"Th" → ""^224"Ra"^(∗) + alpha`

`""^224"Ra"^(∗) → ""^224"Ra" + γ (217 "keV")`.

Atomic mass of ²²⁸Th is 228.028726 u, that of ²²⁴Ra is 224.020196 u and that of  `""_2^4H` is 4.00260 u.

(Use Mass of proton m_p = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_n = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c²,1 u = 931 MeV/c².)

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:
¹²N → ¹²C* + e⁺ + v
¹²C* → ¹²C + γ (4.43MeV).
The atomic mass of ¹²N is 12.018613 u.

(Use Mass of proton m_p = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_n = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c²,1 u = 931 MeV/c².)

The decay constant of `""_80^197`Hg (electron capture to `""_79^197`Au) is 1.8 × 10⁻⁴ S⁻¹. (a) What is the half-life? (b) What is the average-life? (c) How much time will it take to convert 25% of this isotope of mercury into gold?

The decay constant of ²³⁸U is 4.9 × 10⁻¹⁸ S⁻¹. (a) What is the average-life of ²³⁸U? (b) What is the half-life of ²³⁸U? (c) By what factor does the activity of a ²³⁸U sample decrease in 9 × 10⁹ years?

⁵⁷Co decays to ⁵⁷Fe by β⁺- emission. The resulting ⁵⁷Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β⁺- decay is 270 days and that of the γ-emissions is 10⁻⁸ s. A sample of ⁵⁷Co gives 5.0 × 10⁹ gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 10⁹per second?

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ¹⁴C per gram per minute. A sample from an ancient piece of charcoal shows ¹⁴C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ¹⁴C is 5730 y.

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t_1/2. Show that after a time t >> t_1/2 the number of active nuclei will become constant. Find the value of this constant.

Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.

The half-life of ⁴⁰K is 1.30 × 10⁹ y. A sample of 1.00 g of pure KCI gives 160 counts s⁻¹. Calculate the relative abundance of ⁴⁰K (fraction of ⁴⁰K present) in natural potassium.

Identify the logic gate represented by the circuit as shown and write its truth table.

Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?

The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.

What will be the values of input A and B for the Boolean expression `overline ((A +B) .(A*B)) =1?`

The output of an OR gate is connected to both the inputs of a NAND gate Draw the logic circuit of this combinaion of getes and write its truth table.

The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0 × 10⁻⁶ C. It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude 2.5 × 10⁴ NC⁻¹ is switched on. How much time will it now take to complete 20 oscillations? 

If the above capacitor is connected across a 6⋅0 V battery, find (a) the charge supplied by the battery, (b) the induced charge on the dielectric and (c) the net charge appearing on one of the coated surfaces.