Advertisements
Advertisements
प्रश्न
Find the Q-value and the kinetic energy of the emitted α-particle in the α-decay of `""_88^226 "Ra"`.
Given `"m"(""_88^226"Ra")` = 226.02540 u, `"m"(""_86^222 "Rn")` = 222.01750 u,
`"m"(""_86^220 "Rn")`= 220.01137 u, `"m"(""_84^216 "Po")`= 216.00189 u.
Advertisements
उत्तर
Alpha particle decay of `""_88^226"Ra"` emits a helium nucleus. As a result, its mass number reduces to (226 − 4) 222 and its atomic number reduces to (88 − 2) 86. This is shown in the following nuclear reaction.
\[\ce{^226_88 Ra -> ^222_86 Ra + ^4_2He}\]
Q-value of
emitted α-particle = (Sum of initial mass − Sum of final mass) c2
Where,
c = Speed of light
It is given that:
`"m"(""_88^226"Ra")` = 226.02540 u
`"m"(""_86^222"Rn")` = 222.01750 u
`"m"(""_2^4"He")` = 4.002603 u
Q-value = [226.02540 − (222.01750 + 4.002603)] u c2
= 0.005297 u c2
But 1 u = 931.5 MeV/c2
∴ Q = 0.005297 × 931.5 ≈ 4.94 MeV
Kinetic energy of the α-particle = `("Mass number after decay"/"Mass number before decay") xx "Q"`
` = 222/226 xx 4.94 = 4.85 " MeV"`
संबंधित प्रश्न
Boron has two stable isotopes, `""_5^10"B"` and `""_5^11"B"`. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of `""_5^10"B"` and `""_5^11"B"`.
The three stable isotopes of neon: `""_10^20"Ne"`, `""_10^21"Ne"` and `""_10^22"Ne"` have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.
Potassium-40 can decay in three modes. It can decay by β−-emission, B*-emission of electron capture. (a) Write the equations showing the end products. (b) Find the Q-values in each of the three cases. Atomic masses of `""_18^40Ar` , `""_19^40K` and `""_20^40Ca` are 39.9624 u, 39.9640 u and 39.9626 u respectively.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
Nuclear species or nuclides are shown by the notation ________ where X is the chemical symbol of the species.
\[\ce{^197_79Au}\] contains ______.
The nuclei of isotopes of a given element contain the same number of ______.
All nuclides with same mass number A are called ______.
A nucleus of mass number A has a radius R such that ______.
A nucleus yYx emits one α and two β particles. The resulting nucleus is ______.
Two cars of mass m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles at the same time t. The ratio of their centripetal acceleration is:
Deuteron is a bound state of a neutron and a proton with a binding energy B = 2.2 MeV. A γ-ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident γ-ray. If E = B, show that this cannot happen. Hence calculate how much bigger than B must E be for such a process to happen.
Two nuclei have different mass numbers A1 and A2. Are these nuclei necessarily the isotopes of the same element? Explain.
Two nuclei may have the same radius, even though they contain different numbers of protons and neutrons. Explain.
Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of ______.
Which of the following are the constituents of the nucleus?
What conclusion is drawn from Rutherford’s scattering experiment of α-particles?
What is ‘Pair production’?
