Question

11. (8 points) Fill in the blanks to complete each of the following nuclear reactions. - - 233 Ac + He 2. Ca + - - 1K c. 20. Au → 291 Hg + d. 18; Eu → __ thiB 12. (10 points) The molar nuclear mass of boron-10 is 10.012937 g/mol. The molar mass of a proton is 1.007825 g/mol. The molar mass of a neutron is 1.008665 g/mol. Calculate the binding energy (in J/mol) of B-10.

Could you please explain in detail how to do these questions? Thank you in advance.

Answer 1

Consider reaction, _Z ^A X $\rightarrow$ ₈₉ ²²³ Ac + ₂⁴ He  

For balanced nuclear reaction, total Z on L.H.S = Total Z on R.H.S

& Total A on L.H.S = Total A on R.H.S

On equating atomic numbers on both sides, we get Z = 89 + 2

i e Z = 91

On equating mass numbers on both sides, we get A =223 + 4 = 227

Element with atomic number 91 is Pa. Hence, balanced nuclear equation is ₉₁ ²²⁷ Pa  $\rightarrow$₈₉ ²²³ Ac + ₂⁴ He

b)   Consider reaction,₂₀ ⁴¹ Ca + _Z ^A X $\rightarrow$ ₁₉ ⁴¹ K

On equating atomic numbers on both sides, we get 20 + Z = 19

$\therefore$ Z = 19 -20 = -1

On equating mass numbers on both sides, we get 41 + A = 41

$\therefore$ A = 41 - 41 = 0

Hence, _Z ^A X = _-1⁰ e  

Hence, balanced nuclear equation is ₂₀ ⁴¹ Ca + _-1 ⁰ e $\rightarrow$ ₁₉ ⁴¹ K

C)

₇₉ ²⁰¹ Au $\rightarrow$ ₈₀²⁰¹Hg + _Z ^A X

On equating atomic numbers on both sides, we get 79 = 80 + Z

$\therefore$ Z = 79 - 80 = -1

On equating mass numbers on both sides, we get 201 = 201 + A

$\therefore$ A = 201 - 201 = 0

Hence, _Z ^A X = _-1⁰ e  

Hence, balanced nuclear equation is ₇₉ ²⁰¹ Au $\rightarrow$ ₈₀²⁰¹Hg +  _-1 ⁰ e

d)

₆₃¹⁵⁰ Eu $\rightarrow$ _Z ^A X + ₊₁⁰_$\beta$

On equating atomic numbers on both sides, we get 63 = Z + 1

$\therefore$ Z = 63 -1 = 62

On equating mass numbers on both sides, we get 150 = A + 0

$\therefore$ A = 150

Element with atomic number 62 is Sm.

Hence, balanced nuclear equation is ₆₃¹⁵⁰ Eu $\rightarrow$ ₆₂¹⁵⁰Sm + ₊₁⁰_$\beta$

Question 12

Boran-10 contain 5 protons and 5 neutrons.

Mass defect =[ [ 5 ( 1.007825 ) + 5 ( 1.008665 ) ] - 10.012937 ] amu

Mass defect = [10.08245 - 10.012937 ] g / mol = 0.069513 amu

We have relation , 1 amu = 1.6605 $\times$ 10 ^-27 kg

We can calculate B.E from the mass defect using the mass-energy equation.E = m c ²

E = [0.069513 amu ( 1.6605 $\times$ 10 ^-27 kg / 1 amu ) ]( 2.998 $\times$ 10 ⁸ m /s ) ²      

E = 1.037 $\times$ 10 ^-11 J per nucleus.

In 1 mole B , there are 6.022 $\times$ 10 ²³ nucleii.

Therefore, B,E in J / mol = ( 1.037 $\times$ 10 ^-11 J / nucleus ) ( 6.022 $\times$ 10  ²³ nucleus ) = 6.248 $\times$ 10 ¹² J / mol

ANSWER : B.E in J / mol = 6.248 $\times$ 10 ¹² J / mol