Question

A$\mathbf{\text{100W}}$lamp has a steady current of$\mathbf{\text{0.83A}}$in its filament. How long is required for$\mathbf{\text{1mol}}$of electrons to pass through the lamp?

Short answer

The time taken by one mole of electrons to pass through the lamp is$\Delta t=1.3days$

Step-by-step solution

Given

Current,$i=0.83\text{\hspace{0.17em}A}$,

Power,$P=100\text{\hspace{0.17em}W}$,

$1\text{mole}=6.02\times {10}^{23}\text{\hspace{0.17em}atoms}$

Understanding the concept

The rate at which the energy is transferred between two bodies is known as power. It can also be defined as the amount of energy $\mathbf{\left(}\mathbf{E}\mathbf{\right)}$ transferred from one body to another in the unit time interval.

$\mathbf{P}\mathbf{=}\frac{E}{t}$

Here, t is the time taken to transfer energy$\mathbf{\left(}\mathbf{E}\mathbf{\right)}$ .

Calculate the time required for 1 mol of electrons to pass through the lamp

Electric current $\left(i\right)$is the rate of transfer of charge with respect to time.

$i=\frac{\Delta q}{\Delta t}$

If $i=0.83\text{\hspace{0.17em}A}$, the time it takes for one mole of electron to pass through the lamp is

$\begin{array}{c}\Delta t=\frac{\Delta q}{i}\\ =\frac{(6.02\times {10}^{23})(1.60\times {10}^{-19}\text{\hspace{0.17em}C})}{0.83\text{A}}\\ =1.16\times {10}^5\text{\hspace{0.17em}sec}\\ \text{=1.34\hspace{0.17em}days}\end{array}$

One mole of electrons can pass in$1.34\text{\hspace{0.17em}days.}$