Q.37. A solution containing active cobalt 60/27 Co having activity of 0.8 µCi and decay constant λ is injected in an animal's body. If 1 cm^{3} of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1 Ci = 3.7 x 10^{10} decays per second and at t = 10 hrs e^{–λt} = 0.84) [2018]
(1) 4 liters
(2) 5 liters
(3) 6 liters
(4) 7 liters
Ans: (2)
(dn/dt) = −λN_{o}
0.8 µ Ci = −λN_{o}
N_{1} = N_{o}(0.84)
v → N_{1}
v cm^{3} → N_{1}/v
v = 3.7/5 × 0.84 × 0.84 × 10^{4} cm^{3}
= 0.5 × 10^{4} cm^{3} = 5 × 10^{3 }cm^{3} = 5 lit
Q.38. The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is: [2018]
(1) 109 eV
(2) 79 eV
(3) 20 eV
(4) 34 eV
Ans. (3)
E_{1} = ionization energy of ionized He
E_{2} = 2. 2E_{2}
E_{1} = 13.6 eV
E_{2} = 13.6/2.2 = 6.18 eV
Total = E_{1} + E_{2} = 13.6 ev + 6.18 eV
E_{Total} = 20 eV
Q.39. At some instant a radioactive sample S_{1} having an activity 5 μCi has twice the number of nuclei as another sample S_{2} which has an activity of 10 μCi. The half lives of S_{1} and S_{2} are: [2018]
(1) 5 years and 20 years, respectively
(2) 20 years and 5 years, respectively
(3) 20 years and 10 years, respectively
(4) 10 years and 20 years, respectively
Ans: (1)
Given : N_{1} = 2N
Hence,
The half life of S_{1 }is 5 years, and
The half life of S_{2 }is_{ }20 years
Q.40. The deBroglie wavelength (λ_{B}) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λG) by: [2018]
(1) λ_{B} = 3λ_{G}
(2) λ_{B} = 2λ_{G}
(3) λ_{B} = 3λ_{G/3}
(4) λ_{B} = 3λ_{G/2}
Ans: (1)
Q.41. Both the nucleus and the atom of some element are in their respective first excited states. They get deexcited by emitting photons of wavelengths λ_{N},λ_{A} respectively. The ratio λ_{N}/λ_{A} is closest to: [2018]
(1) 10^{–1}
(2) 10^{–6}
(3) 10
(4) 10^{–10}
Ans: (2)
where Ea and EN are energies of photons from atom and nucleus respectively. EN is of the order of MeV and Ea in few eV.
So
Q.42. An electron beam is accelerated by a potential difference V to hit a metallic target to produce Xrays. It produces continuous as well as characteristic Xrays. If λ_{min} is the smallest possible wavelength of Xray in the spectrum, the variation of log λ_{min} with log V is correctly represented in [2017]
(1)
(2)
(3)
(4)
Ans: (3)
In Xray tube
Slope is negative
Intercept on yaxis is positive
Ans: (4)
Ans: (2)
From energy level diagram
Ans: (4)
(2)
(3)
(4)
Ans: (2)
F_{e} = F_{n} = 0
F_{e} = –F_{m}
Ans: (3)
s = e (n_{e}μ_{e} + n_{n}μ_{n})
= 1.6 × 10^{19} (5 × 10^{18} × 2 + 5 × 10^{19} × 0.01)
= 1.6 × 10^{–19} (10^{19} + 0.05 × 10^{19})
= 1.6 × 1.05
= 1.68
Ans: (4)
=1/5 = 0.2
Frequency = 12 × 10^{3} kHz
F = 12.00 kHz
F_{1} = 1200 – 20 = 1180 kHz
F_{2} = 1200 + 20 = 1220 kHz
Q.49. A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is: [2017]
(1) away from the wire
(2) towards the wire
(3) parallel to the wire along the current
(4) parallel to the wire opposite to the current
Ans: (1)
Ans: (2)
a = 0.1 mm = 10^{–4}
λ = 6000 × 10^{10}
= 6 × 10^{7}
D = 0.5 m
for 3^{rd} dark
a sin θ = 3λ
(2)
(3)
(4)
Ans: A
.... (i)
...... (ii)
(ii)  (i) gives
.... (iv)
combining (iii) & (iv)
Ans: D
80 minutes = 4 halflives of A = 2 halflives of B
Let the initial number of nuclei in each sample be N
NA after 80 minutes = N/2^{4}
⇒ Number of A nuclides decayed = 15/16N
NB after 80 minutes = N/2^{2}
⇒ Number of B nuclides decayed = 3/4N
Required ratio =
Ans: (1)
Energy of proton = 13.6 – 3.4 = 10.2 eV
For removal of electron
so minimum value of n = 4
Ans: (1)
using these equations
Ans. (2)
Energy of microwaves lie in range of vibration energy of water molecules.
Ans: (3)
Assuming perfectly inelastic collision for maximum loss in K.E.
⇒ K.E_{i} ≥ 20.4 eV
Ans: (4)
...(1)
...(2)
(Equating (i) & (ii))
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