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One mole of alpha particles has a charge of ____________
Choose the correct option.
A. $+2$ units
B. $+1$ units
C. $+2$ faraday
D. $+2$ coulombs

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Last updated date: 21st Feb 2024
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Hint: This question is based on the mole concept and simple unitary method calculation. To solve it, we firstly need to find out the number of protons in one mole of alpha particles. We know that one proton has a charge $1.6\times {{10}^{-19}}C$. So, if we multiply this charge with the total number of protons in alpha particles, we will get the total charge in one mole of alpha particles.

Complete step-by-step answer:Let us firstly understand, what do we mean by alpha particles.
Alpha particles are positively charged helium atoms, which are emitted through the decay of different radioactive substances.
We should remember that an alpha particle is a helium atom with $\left( +2 \right)$charge in it. Let us see what charge we are referring to.
We know that a helium atom has 2 electrons revolving around the nucleus which contains 2 protons and 2 neutrons. Now, alpha particles can be represented as $H{{e}^{2+}}$. This means that the helium atom has lost its 2 electrons and hence there are no electrons left in it. The only subatomic particles present in it are 2 protons and 2 neutrons. We also know that neutrons have no charge. So, in $H{{e}^{2+}}$the charge is constituted by only 2 protons present in it, which is represented by +2 as protons have positive charge.
So, we can say that one mole of alpha particles has 2 moles of protons in it.
We already know that charge of one proton = $1.6\times {{10}^{-19}}C$.
Therefore, charge in one mole of protons = $1.6\times {{10}^{-19}}C\times 6.02\times {{10}^{23}}=96500C$
Therefore, charge on two moles of protons will be given as = (2 $\times $charge on one mole of proton)
$\begin{align}
  & =2\times 96500 \\
 & =193000C \\
\end{align}$
Hence, we can see that charge on two moles of protons or to be more precise, charge on one mole of alpha particles is $193000C$.
We can see that none of the options matches this answer, so we need to convert it to another unit.
Let us convert the coulombs in Faraday.
We should remember that $\text{1 Coulomb = }\dfrac{\text{1}}{96500}\text{Faraday}$
Therefore, $\text{193000 C = }\dfrac{193000}{96500}=2\text{faraday}$

Hence, the option C is the correct option.

Note: Alpha particles have short range of absorption and they cannot penetrate the outer skin of the human body. Hence, they are not dangerous to life until and unless their source is ingested. While solving the question always determine your starting and ending point, and perform the calculations properly.
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