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gf $_{92}U^{238} undergoes succesively $8 \alpha$ decays and $6 \beta$ decays then resulting nucleus is
$_{92}U^{238} \rightarrow _{76}X^{206} \rightarrow _{82}Y^{206}$ $ \therefore _{82}Pb^{206}\; _{or}Pb^{206}$
The energy released by the fission of one unanium atom is 200 MeV. The number of fission Per second required to Produce 3.2 w of Power is
Energy released per uranium atom = 200 MeV $= 200\times 10^6 ev = 200 \times 10^6 \times 1.6 \times 10 ^{-19}= 320\times10^{-13} \gamma $ $For 320 \times 10^{-13} 2 \rightarrow 1 atom$ $32 J \rightarrow \lambda {3.2 \over 320 \times 10^{-13}} =10^{11}atoms$
The energy difference between the first two leVels of hydrogen atom is 10.2 eV. what is the corresponding energy difference for a singly ionised helium atom?
The energyleVel of hydrogen atom corresponding to 10.2 eV is n= 2, n = 1 correponding engery for the level of helium atom $ E = {-13.6 Z^2 \over n^2}$ $ \triangle E = E_2^1 - E_1^1 $ $ \triangle E = {13.6 \times 4 \over 4} - { (-13.6 \times 4) \over 1 } = -13.6 + 54.4 = 40.8 eV$
The total energy of the electron in the first excited state of hydrogen is -3.4 eV. what is the kinetic energy of the electron in this state?
For any state K.E = $ {1 \over 8 \pi E_0} {Ze^2 \over Cn} and cangatoms 1$ $P.E = -{1 \over 4 \pi \epsilon_0 }{Ze^2 \over rn } (total energy in the state )$ E = K.E + P.E $E = -{ 1 \over {8 \pi \epsilon _0 }} {Ze^2 \over ru} = -K.E $
The wave length of second line of Balmer series is 486.4 nm. what is the wave length of the first line of lyman saries ?
For wave length of second line of Balmer series $ {1\over \lambda_{2(B)}} = R [ {1\over 2^2} - {1\over 4^2}] = R [{1\over 4} - {1\over 16}] = {3R \over 16}$ $ \Rightarrow \lambda2(B) = {16\over 3R}$ For wave length of First line of Luman series $ {1\over \lambda_{2(L)}} = R [ {1\over 1^2} - {1\over 2^2}] = R [{1\over 1} - {1\over 4}] = {3R \over 4}$ $ \lambda_1(L) = {4\over 3R}$ $ {\lambda_2(B) \over \lambda_1(L)} = {16 \over 3R} \times {3R \over 4 } = 4 $ $ \lambda_1(C) = {\lambda_2(B)\over 4} = {486.4 \over 4 } = 121.6 mm$
The innermost orbit of the hydrogen atom has a radius 0.53 A. what is radius of 2nd orbit is ?
$ r \,\alpha {n^2 \over z } $ For hydrogen atom Z = 1 $ r \,\alpha \, n^2 $ $ {r_1 \over r_2 } = {(1 \over 4 )}$ $ r_2 = 4r_1 = 4 \times 0.53 A = 2.12 A $
If a hydrogen atom emits a Photon of wave length, the recoil speed of the atom of mass m is given by
According comservation of momentum momentum of photon = momentum of rocil atom. ${h \over \lambda} = m\vartheta $ $\therefore \vartheta = { h\over m \lambda}$
A thief was planning to rob the minister's house located 100m away from his home.he started moving with a constant speed of 3m/s.on seeing a police jeep at exact mid way he started running back to his home with a speed of 9 m/s. the average speed and average velocity repectively in m/s is
average speed is the ratio of total distance travelled to the total time taken .since initial and final position is the same average velocity is zero
The size of the nucleus is of the order of
The size of a nucleus is generally of the order of $10^{-14}$ meters. This is much smaller than the size of an atom, which is of the order of $10^{-10}$ meters. The nucleus is composed of protons and neutrons and is densely packed.
The ratio of atomic volume of nuclear volume is of the order of
The ratio of the atomic volume to the nuclear volume is of the order of $10^{15}$. This is because the atomic volume is determined by the electron cloud, which is much larger in size compared to the densely packed nucleus.
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