Question

which of the following species has maximum charge to mass ratio a)deuterium b)hydrogen c)helium^+ d) helium ^+2

Answer 1

i think a is the answer is deuterium as heigher mass but lesser charge .

Answer 2

Answer: Option (b) is the correct answer.

Explanation:

A deuterium means $^{2}_{1}H$[/tex]. It contains 2 times the mass of an electron and since it has only one electron or proton. So, charge will be 1 times charge of an electron.

Therefore, its mass will be $2 \times 9.1 \times 10^{-31}$ = $18.2 \times 10^{-31}$. And, charge will be $1 \times 1.6 \times 10^{-19}$.

Charge to mass ratio of deuterium is $8.8 \times 10^{10}$.

Similarly, hydrogen atom means $^{1}_{1}H$. So, there is just one electron and mass is also 1 times the mass of an electron. Hence, its charge to mass ratio is $\frac{1 times 1.6 \times 10^{-19}}{1 times 9.1 \times 10^{-31}}$.

Therefore, for hydrogen charge to mass ratio is $0.17 \times 10^{12}$ or $17 \times 10^{10}$.

Helium is $^{4}_{2}He$. $He^{+}$ means there is only one electron. So, mass will be $4 \times 9.1 \times 10^{-31}$ = $36.4 \times 10^{-31}$. And, charge will be $1 \times 1.6 \times 10^{-19}$.

Charge to mass ratio of helium is $0.043 \times 10^{12}$ or $4.3 \times 10^{10}$.

Whereas $He^{2+}$ means there are two electrons. So, mass will be $4 \times 9.1 \times 10^{-31}$ = $36.4 \times 10^{-31}$. And, charge will be $0 \times 1.6 \times 10^{-19}$.

Charge to mass ratio of helium is 0.

Thus, we can conclude that hydrogen has maximum charge to mass ratio.