Advertisements
Advertisements
Question
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
Solution
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"`
RELATED QUESTIONS
A nucleus with mass number A = 240 and BE/A = 7.6 MeV breaks into two fragments, each of A = 120 with BE/A = 8.5 MeV. Calculate the released energy.
Two stable isotopes of lithium `""_3^6"Li"` and `""_3^7"Li"` have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.
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.
Name a material which is used in making control rods in a nuclear reactor.
Write one balanced equation to show Emission of `beta^-` (i.e. a negative beta particle)
Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number A.
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.)
Find the Q-value and the kinetic energy of the emitted α-particle in the α-decay of `""_86^220"Rn"`.
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.
Atomic mass unit (u) is defined as ________ of the mass of the carbon (12C) atom.
A vessel contains oil (density 0.8 g/cm3) over mercury (density 13.6 g/cm3). A sphere of homogeneous composition floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g/cm3 is ______.
The mass number of a nucleus is equal to the number of:-
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.
Distinguish between isotopes and isobars.
James Chadwick, in 1932 studied the emission of neutral radiations when Beryllium nuclei were bombarded with alpha particles. He concluded that emitted radiations were neutrons and not photons. Explain.
What conclusion is drawn from Rutherford’s scattering experiment of α-particles?
The volume occupied by an atom is greater than the volume of the nucleus by a factor of about:
The density of nuclear matter is:
1 amu is defined as:
