If a doubly-ionized oxygen atom (O–2) is accelerated from rest by going through a potential difference of 20 V, what will be the change in its kinetic energy?
40 ev
To find the change in kinetic energy of the doubly-ionized oxygen atom, we need to use the equation:
ΔKE = qΔV
where ΔKE is the change in kinetic energy, q is the charge of the particle, and ΔV is the potential difference.
For an ionized oxygen atom (O–2), the charge is 2 times the elementary charge (e) since it is doubly-ionized. The elementary charge is approximately 1.6 x 10^-19 C.
So, q = 2e = 2 * 1.6 x 10^-19 C = 3.2 x 10^-19 C
Given that the potential difference is 20 V,
ΔV = 20 V
Plugging in the values into the equation, we find:
ΔKE = (3.2 x 10^-19 C) * (20 V)
Calculating the product:
ΔKE = 6.4 x 10^-18 J
Therefore, the change in kinetic energy of the doubly-ionized oxygen atom is 6.4 x 10^-18 Joules.
To find the change in kinetic energy, we need to calculate the final kinetic energy and subtract the initial kinetic energy.
The kinetic energy of an object is given by the equation:
K = (1/2)mv^2
Where:
K is the kinetic energy
m is the mass of the object
v is the velocity of the object
Since we know that the oxygen atom is accelerated from rest, the initial velocity (v_i) is zero.
Next, we need to determine the final velocity (v_f) using the potential difference (ΔV) and the charge of the oxygen ion (e).
The potential energy difference (ΔV) is given by the equation:
ΔV = eV
Where:
ΔV is the potential difference
e is the elementary charge (1.6 x 10^-19 C)
V is the voltage applied
In this case, the oxygen ion has a charge of 2e (-2 times the elementary charge), so the potential energy difference can be calculated as:
ΔV = (2e)V = (2)(1.6 x 10^-19 C)(20 V) = 6.4 x 10^-18 J
Now, we can calculate the final kinetic energy (K_f) using the conservation of energy principle:
K_f + U_f = K_i + U_i
Since the initial potential energy (U_i) and final potential energy (U_f) are both zero, we can simplify the equation to:
K_f = K_i + ΔK
Where ΔK represents the change in kinetic energy.
Since the initial kinetic energy (K_i) is zero, we can further simplify the equation to:
K_f = ΔK
So, the change in kinetic energy is equal to the final kinetic energy.
Now, we substitute the known values into the equation:
ΔK = (1/2)mv^2
Since we do not know the mass of the oxygen ion, we cannot calculate the exact value of the change in kinetic energy without that information. However, we can still provide the formula to calculate the change in kinetic energy once the mass is known.
Just plug in the mass into the equation, along with the final velocity (which we will obtain by solving for it using the conservation of energy principle), and you will find the change in kinetic energy.