The voltage across the cell membrance is 0.070 V
the cell membrane is 0.10 µm thick
what is the work done in joules to move one sodium ion (charge= 1.6 x 10 ^-19 C) from inside the cell to outside the cell?
To calculate the work done in joules to move one sodium ion from inside the cell to outside the cell, we need to use the formula:
Work (W) = Charge (Q) × Voltage (V)
Given:
Voltage across the cell membrane (V) = 0.070 V
Thickness of the cell membrane (d) = 0.10 µm
Charge of the sodium ion (Q) = 1.6 × 10^-19 C
First, we need to convert the thickness of the cell membrane from micrometers (µm) to meters (m) since the unit of voltage is in volts (V). There are 1 × 10^-6 meters in 1 µm.
Thickness (d) = 0.10 × 10^-6 meters
Next, since the voltage represents the potential difference across the cell membrane, we multiply it by the charge to get the work done.
Work (W) = (Charge (Q) × Voltage (V))
Work (W) = (1.6 × 10^-19 C) × (0.070 V)
The work (W) will be in joules (J).
Let's calculate the work done:
Work (W) = (1.6 × 10^-19 C) × (0.070 V)
Work (W) = 1.12 × 10^-20 J
Therefore, the work done in joules to move one sodium ion from inside the cell to outside the cell is 1.12 × 10^-20 J.