Question

In a neon discharge tube \[2.8 \times {\text{ }}{10^{18}}N{e^ + }\]\[Ne\]” ions move to the right per second while \[1.2 \times {10^{18}}\] electrons move to the left per second. Therefore the current in the discharge tube is:
A) \[0.64A\] towards right
B) \[0.256A\] towards right
C) \[0.64A\] towards left
D) \[0.256A\] towards left

Answer 1

Hint: Here we have to find out the current in the discharge tube. Also, we must remember that the current flows in the opposite direction of motion of the electron.
Then we use the formula for current and putting the values. After doing some simplification we get the current. Finally we get the required answer.

Formula used:
\[I = \dfrac{{n \times q}}{t}\]
Where,
\[I\]= the current flow in the tube
\[n\]= number of ions,
$q$= charge of ions
$t$=time.

Complete step by step answer:
The net current flowing in a tube is caused by a positive charge and electrons. And the current flows in the opposite direction of motion of the electron.
Let, the current flowing due to positive ions is \[{I_1}\] and the current flowing due to electrons is \[{I_2}\]. Since the current is the rate of charge per unit time, the total charge will be \[{I_1} + {I_2}\].
Now,
rate of flow of charge, of \[N{e^ + }\] ions, is
\[{I_1} = \dfrac{{n \times {q_{ne}}}}{t}\]
given,
\[n = 2.8 \times {10^{18}}\]
\[ \Rightarrow {q_{ne}} = 1.6 \times {10^{ - 19}}\]
\[ \Rightarrow t = 1\]
\[ \Rightarrow {I_1} = 2.8 \times {10^{18}} \times 1.6 \times {10^{ - 19}}\]
\[ \Rightarrow {I_1} = 0.448\]
rate of flow of charge, of the electrons, is
\[ \Rightarrow {I_2} = \dfrac{{n \times e}}{t}\]
given,
\[n = 1.2 \times {10^{18}}\]
\[e = 1.6 \times {10^{ - 19}}\]
\[ \Rightarrow t = 1\]
\[ \Rightarrow {I_2} = 1.2 \times {10^{18}} \times 1.6 \times {10^{ - 19}}\]
\[ \Rightarrow {I_2} = 0.192\]
So, the total charge
\[ \Rightarrow {I_1} + {I_2} = 0.448 + 0.192\]
\[ \Rightarrow {I_1} + {I_2} = 0.64\]
So, the current in the discharge tube is \[0.64\]. The direction is towards the right because here the direction of the electron is towards the left and the current flows in the opposite direction of the motion of the electron.

Hence option (A), \[0.64A\] towards right is the correct answer.

Note: For Ne+ the charge should be \[q = 1 \times 1.6 \times {10^{ - 19}}\]. But if we get Ne2+ the charge is taken \[q = 2 \times 1.6 \times {10^{ - 19}}\].
The direction of the current must be put or understood properly and can be calculated through a simple algebraic method as the current is a scalar quantity.
Neon is considered as the second lightest noble gas that is used to fill in the neon lamps and the discharge tubes and the gas lasers are made with the help of neon and helium.