physics

Question

Use the information below to answer the following 2 questions:

The mass of one nucleus of potassium-40 was measured to be 39.9687 u.  

Notes:

• The speed of light that should be used is 3.00x10⁸ m/s.
• u= 1.66x10^-27kg

 

 

 

1
 

 

Question 4 options:

The mass defect for potassium-40 is: -___x10^-28kg. 

 

 

 

2

 

 

Question 5 options:

The binding energy for potassium-40 is: -___x10^-11J. 

 

Answer 1

(1)

The nuclear mass of the Potassium is 39.9687 u

In a potassium K-40, there are 19 protons and 21 neutrons.

From the table,

The mass of each proton is 1.007276

The mass of each electron is 1.008665

 

Mass defect:

The difference between the mass of the atom and the sum of the masses of individual proton, electron and neutron is called  the  mass  defect  (Dm).

Dm = (Number of Proton * mass of each proton) + (Number of Neutron * mass of each Neutron) - Mass of the atom

Dm = (19*1.007276) + (21 * 1.008665) - (39.9687)

Dm = 19.138244 + 21.181965 - 39.9687

Dm =  0.3515 amu

We know that 1 amu = 1.66053892 × 10^-27 kilograms

Dm =  0.3515 * 1.66053892 × 10^-27 kilograms

Dm =  0.5836 * 10^-27 kg

Dm =  5.836 * 10^-28 kg

Therefore the mass defect of the potassium -40 is  5.836 * 10^-28 kg.

Answer 2

(2)

Mass defect of the potassium -40 is  5.836 * 10^-28 kg.  [From (1)]

Speed of the light is 3 * 10⁸ m/sec.

Binding energy = mC²

Binding energy = 5.836 * 10^-28 * 3 * 10⁸ 

E = 5.2524 * 10^-11 J

Therefore binding energy of Potassium -40 is 5.2524 * 10^-11 J.