Question

example problem 2: how many neutrons are in 2.5 kg of neutrons? given: m = 2.5 kg, $m_n = 1.675 \times 10^{-27}$ kg find: n = ? neutrons eqn: $n = m/m_n$

Explanation:

Step1: Identify the formula

We use the formula \( N=\frac{m}{m_n} \), where \( m = 2.5\space kg \) is the total mass and \( m_n=1.675\times 10^{-27}\space kg \) is the mass of one neutron.

Step2: Substitute the values

Substitute \( m = 2.5\space kg \) and \( m_n = 1.675\times 10^{-27}\space kg \) into the formula:
\( N=\frac{2.5}{1.675\times 10^{-27}} \)

Step3: Calculate the result

First, calculate \( \frac{2.5}{1.675}\approx1.4925 \). Then, divide by \( 10^{-27} \) which is equivalent to multiplying by \( 10^{27} \). So \( N\approx1.4925\times 10^{27}\approx1.5\times 10^{27} \) (rounded to two significant figures) or more precisely \( N=\frac{2.5}{1.675\times 10^{-27}}=\frac{2.5\times 10^{27}}{1.675}\approx1.4925\times 10^{27}\approx1.5\times 10^{27} \)

Answer:

The number of neutrons is approximately \( \boldsymbol{1.5\times 10^{27}} \) (or more precisely \( \approx1.49\times 10^{27} \))