Answer
414.6k+ views
Hint:In order to solve part (a) calculate the total mass of nuclei before reaction and total mass of product nuclei and nucleons and compare them.
(b) For part (b) first calculate radius of nucleus and volume of nucleus and put in formula of nuclear density which is
$d = \dfrac{m}{V}$
Where
m $ = $ mass of nucleus
V $ = $ volume of nucleus
Complete step by step answer:
(a) Mass of tangent nucleus ${(_1}{H^2}){m_t} = 2.0147amu$
Mass of bombarding nucleus ${(_1}{H^2}){m_b} = 2.0147amu$
Mass of product nucleus ${(_2}H{e^4}){m_\rho } = 3.0169amu$
Mass of outgoing particle ${(_0}{n^1}){m_n} = 1.0087amu$
So, ${m_t} + {m_b} = 2.0147 + 2.0147$
$\Rightarrow {m_t} + {m_b} = 4.0294amu$
$\Rightarrow {m_\rho } + {m_n} = 3.0169 + 1.0087$
$\Rightarrow {m_\rho } + {m_n} = 4.0256amu$
Hence $({m_t} + {m_b}) - ({m_\rho } + {m_n}) = 0.0038amu$
i.e.., $({m_t} + {m_b}) > ({m_\rho } + {m_n})$
So, this extra mass is counter into energy and this energy is released although a number of nucleons are consumed.
(b) The radius of nucleus is given as
$\Rightarrow R = {R_0}{A^{1/3}}$
Where
$\Rightarrow {R_0} = $ Fermi radius
A $ = $ Mass number
So, the volume of nucleus
$\Rightarrow V = \dfrac{4}{3}\pi {R^3}$
$\Rightarrow V = \dfrac{4}{3}\pi {({R_0}{A^{1/3}})^3}$
$\Rightarrow V = \dfrac{4}{3}\pi R_0^3A$
$\Rightarrow V \propto A$ …..(1)
Nuclear density $ = \dfrac{{Mass}}{{Volume}} = \dfrac{m}{V}$
Mass can be written as
$m = A$ $($Mass number$)$
Nuclear density $ = \dfrac{A}{{\dfrac{4}{3}\pi R_0^3A}}$
Nuclear density $ = \dfrac{3}{{4\pi R_0^3}}$
Above expression shows that nuclear density is independent of mass number A.
Note: Many times, students may get confused between isotopes of Hydrogen. So, always remember that hydrogen has three naturally occurring isotopes, $_1^1H,_1^2H$ and $_1^3H$.
The first two of these are stable while $_1^3H$ has a half life of $12.32$ years.
There are also heavier isotopes, which are all synthetic and have a half life less than ${10^{ - 21}}$ second of these $_1^5H$ is the most stable and $_1^7H$ is the least.
(b) For part (b) first calculate radius of nucleus and volume of nucleus and put in formula of nuclear density which is
$d = \dfrac{m}{V}$
Where
m $ = $ mass of nucleus
V $ = $ volume of nucleus
Complete step by step answer:
(a) Mass of tangent nucleus ${(_1}{H^2}){m_t} = 2.0147amu$
Mass of bombarding nucleus ${(_1}{H^2}){m_b} = 2.0147amu$
Mass of product nucleus ${(_2}H{e^4}){m_\rho } = 3.0169amu$
Mass of outgoing particle ${(_0}{n^1}){m_n} = 1.0087amu$
So, ${m_t} + {m_b} = 2.0147 + 2.0147$
$\Rightarrow {m_t} + {m_b} = 4.0294amu$
$\Rightarrow {m_\rho } + {m_n} = 3.0169 + 1.0087$
$\Rightarrow {m_\rho } + {m_n} = 4.0256amu$
Hence $({m_t} + {m_b}) - ({m_\rho } + {m_n}) = 0.0038amu$
i.e.., $({m_t} + {m_b}) > ({m_\rho } + {m_n})$
So, this extra mass is counter into energy and this energy is released although a number of nucleons are consumed.
(b) The radius of nucleus is given as
$\Rightarrow R = {R_0}{A^{1/3}}$
Where
$\Rightarrow {R_0} = $ Fermi radius
A $ = $ Mass number
So, the volume of nucleus
$\Rightarrow V = \dfrac{4}{3}\pi {R^3}$
$\Rightarrow V = \dfrac{4}{3}\pi {({R_0}{A^{1/3}})^3}$
$\Rightarrow V = \dfrac{4}{3}\pi R_0^3A$
$\Rightarrow V \propto A$ …..(1)
Nuclear density $ = \dfrac{{Mass}}{{Volume}} = \dfrac{m}{V}$
Mass can be written as
$m = A$ $($Mass number$)$
Nuclear density $ = \dfrac{A}{{\dfrac{4}{3}\pi R_0^3A}}$
Nuclear density $ = \dfrac{3}{{4\pi R_0^3}}$
Above expression shows that nuclear density is independent of mass number A.
Note: Many times, students may get confused between isotopes of Hydrogen. So, always remember that hydrogen has three naturally occurring isotopes, $_1^1H,_1^2H$ and $_1^3H$.
The first two of these are stable while $_1^3H$ has a half life of $12.32$ years.
There are also heavier isotopes, which are all synthetic and have a half life less than ${10^{ - 21}}$ second of these $_1^5H$ is the most stable and $_1^7H$ is the least.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)