Answer
Verified
400.2k+ views
Hint:It is a numerical question based on the concept of mass defect, and the energy released. With the help of calculation of mass defect, and the energy released; the average power is given; the time required can be calculated. We have the formula of mass defect, i.e.
$\Delta$m = mass of products – mass of reactants. We can use this formula for mass defect.
Complete step by step solution:
> Now, we know that we are given two reactions. In the first reaction, there is formation of a proton, and in the second reaction, there is formation of a helium nucleus, and a neutron.
Thus, by adding these two equations we get,
3($_1$H$^{2}$) $\rightarrow$ $_2$He$^{4}$ + $_0$n$^{1}$ + $_1$H$^{1}$
> Now, the mass of the helium nucleus is 4.014, the deuterium is 2.014, and the neutron has the mass 1.007, and the proton has the mass 1.0008.
- Thus, by using the mass defect, or mass energy conservation; as mentioned i.e. mass defect is equal to mass of the reactants (left-side) subtracted from the mass of products (right-side).
- Therefore, it can be written as
$\Delta$ m = (3 $\times$ 2.014 – 4.001 – 1.007 – 1.0008) = 0.026 amu
> Now, we can calculate the energy released in this equation, i.e.
- Energy released value = 0.026 $\times$ 931 MeV, (1 MeV = 1.6 $\times$ 10$^{-13}$J)
Thus, energy released = 3.87$\times$ 10$^{-12}$ J
- The value of energy released is the consumption of energy by 3 deuteron atoms.
> Now, we have to calculate for the 10$^{40}$ deuterons
Energy released = $\dfrac{10^{40} \times 3.87 \times 10^{-12}}{3}$= 1.29 $\times$ 10$^{28}$ J
- In the question, the average power radiated is given i.e. 10$^{16}$ W, is equal to 10$^{16}$ J/s.
> Now, further let us calculate the time required to exhaust the deuteron supply of star.
We can calculate it by dividing the energy released to that of the average power radiated, i.e. $\dfrac{1.29 \times 10^{28}}{10^{16}}$ = 1.29 $\times$ 10$^{12}$ s =10$^{12}$ s (approx.)
In the last, we can conclude that the deuteron supply of star is exhausted in the time order of 10$^{12}$ Hence, the correct option is (C).
Note: We can calculate the energy consumption of 3 deuteron atoms by mass-energy conservation, i.e. by multiplying the energy released in the formula of mass defect only. There is no need of confusion within the two formulae.
$\Delta$m = mass of products – mass of reactants. We can use this formula for mass defect.
Complete step by step solution:
> Now, we know that we are given two reactions. In the first reaction, there is formation of a proton, and in the second reaction, there is formation of a helium nucleus, and a neutron.
Thus, by adding these two equations we get,
3($_1$H$^{2}$) $\rightarrow$ $_2$He$^{4}$ + $_0$n$^{1}$ + $_1$H$^{1}$
> Now, the mass of the helium nucleus is 4.014, the deuterium is 2.014, and the neutron has the mass 1.007, and the proton has the mass 1.0008.
- Thus, by using the mass defect, or mass energy conservation; as mentioned i.e. mass defect is equal to mass of the reactants (left-side) subtracted from the mass of products (right-side).
- Therefore, it can be written as
$\Delta$ m = (3 $\times$ 2.014 – 4.001 – 1.007 – 1.0008) = 0.026 amu
> Now, we can calculate the energy released in this equation, i.e.
- Energy released value = 0.026 $\times$ 931 MeV, (1 MeV = 1.6 $\times$ 10$^{-13}$J)
Thus, energy released = 3.87$\times$ 10$^{-12}$ J
- The value of energy released is the consumption of energy by 3 deuteron atoms.
> Now, we have to calculate for the 10$^{40}$ deuterons
Energy released = $\dfrac{10^{40} \times 3.87 \times 10^{-12}}{3}$= 1.29 $\times$ 10$^{28}$ J
- In the question, the average power radiated is given i.e. 10$^{16}$ W, is equal to 10$^{16}$ J/s.
> Now, further let us calculate the time required to exhaust the deuteron supply of star.
We can calculate it by dividing the energy released to that of the average power radiated, i.e. $\dfrac{1.29 \times 10^{28}}{10^{16}}$ = 1.29 $\times$ 10$^{12}$ s =10$^{12}$ s (approx.)
In the last, we can conclude that the deuteron supply of star is exhausted in the time order of 10$^{12}$ Hence, the correct option is (C).
Note: We can calculate the energy consumption of 3 deuteron atoms by mass-energy conservation, i.e. by multiplying the energy released in the formula of mass defect only. There is no need of confusion within the two formulae.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE