English
Karnataka Board PUCPUC Science 2nd PUC Class 12

Find the Q-value and the Kinetic Energy of the Emitted α-particle in the α-decay of _88^226 Ra and _86^220rn

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.

Numerical
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"`

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Nuclei - Exercise [Page 463]

APPEARS IN

NCERT Physics Part I and II [English] Class 12
Chapter 13 Nuclei
Exercise | Q 12.1 | Page 463
NCERT Physics Part I and II [English] Class 12
Chapter 13 Nuclei
Exercise | Q 13.12 (a) | Page 463

RELATED QUESTIONS

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"`.


Obtain approximately the ratio of the nuclear radii of the gold isotope `""_97^197 "Au"` and the silver isotope `""_47^197"Ag"`.


The nucleus `""_10^23"Ne"` decays by `beta^(-)`emission. Write down the β decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

`"m"(""_10^23 "Ne")` = 22.994466 u

`"m"(""_11^23 "Na")` = 22.989770 u.


What do you mean by polar molecules and non-polar molecules? Give ‘one’ example each.


Write one balanced equation to show Emission of `beta^-` (i.e. a negative beta particle)


The atomic mass of Uranium `""_92^238"U"` is 238.0508 u, while that of Thorium `""_90^234"Th"` is 234.0436u, and that of Helium `""_2^4"He"` "is 4.0026u. Alpha decay converts `""_92^238"U"` into `""_92^234"Th"` as, shown below:

`""_92^238"U" -> ( ""_90^234"Th" + ""_2^4"He" + "Energy" )`


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.


\[\ce{^197_79Au}\] contains ______.


The nuclei of isotopes of a given element contain the same number of ______.


Nuclides with same neutron number N but different atomic number Z are called ______.


A nucleus of mass number A has a radius R such that ______.


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:-


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.


Which of the following are the constituents of the nucleus?


Assertion (R): Fusion of hydrogen nuclei into helium nuclei is the source of energy of all stars.

Reason (R): In fusion heavier nuclei split to form lighter nuclei.


The density of nuclear matter is:


Energy equivalent of 1 amu is:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×