Question

The unified atomic mass unit is defined to be 1 u = 1.6605 ✕ 10−27 kg. Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for c and |qe|.

Answer 1

Answer: The energy yield is 931.5MeV

Explanation: Please see the attachments below

Answer 2

Answer:

Vₑ = 9.314569 × 10^8 eV

Vₑ = 931.5 ×10^6 eV

Vₑ = 931.5 MeV

Verified

Explanation:

Applying the Einstein equation which shows that energy and mass are interchangeable (related). Which can be written mathematically as;

E = mc^2 ......1

Where E = energy

m = mass

c = speed of light

Energy can also be related to potential difference and charge as;

E = qv ........2

Where;

E = energy

q = charge

v = potential difference

Substituting equation 2 into 1

qv = mc^2

Making v the subject of formula

v = (mc^2)/q .........3

For a unified atomic mass unit is defined to be 1 u = 1.6605 ✕ 10−27 kg

m = 1.6605 × 10^−27 kg

c = 2.9979 × 10^8 m/s

Charge on electron qₑ = 1.6021766 × 10^-19 Coulomb

So, equation 3 becomes;

Vₑ = (mc^2)/qₑ

Substituting the given values;

Vₑ = (1.6605 × 10^−27 kg × (2.9979 × 10^8 m/s)^2)/1.602 1766× 10^-19

Vₑ = 9.314569 × 10^8 eV

Vₑ = 931.5 ×10^6 eV

Vₑ = 931.5 MeV

Verified