Find the Kinetic energy (in keV) of 12 6 C atom of mass 12.0 u whose speed is 2 x 10^6 m/s.
Ke (Kinetic Energy) = (1/2)m*v^2
m = mass
v = speed
u = 1.66 x 10^-27 kg
12u = 1.99 x 10^-26 kg
Ke = (1/2)(1.99 x 10^-26 kg)*(2 x 10^6m/s)^2
Ke = 3.98 x 10^-12. Convert this to KeV or w/e.
To find the kinetic energy (KE) of an object, we can use the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
First, we need to convert the mass of the carbon atom from unified atomic mass units (u) to kilograms (kg):
1 u = 1.66 x 10^-27 kg
Mass of carbon atom = 12.0 u * (1.66 x 10^-27 kg/u) = 1.992 x 10^-26 kg
Next, we need to convert the velocity from meters per second (m/s) to the speed of light (c) units, keV (kiloelectronvolt):
1 m/s = 2.2 x 10^-6 keV
Velocity = 2 x 10^6 m/s * (2.2 x 10^-6 keV/m/s) = 4.4 keV
Now we can calculate the kinetic energy:
KE = (1/2) * mass * velocity^2
KE = (1/2) * (1.992 x 10^-26 kg) * (4.4 keV)^2
Simplifying this expression gives you the value in joules (J), so we need to convert it back to kiloelectronvolt (keV):
1 J = 6.242 x 10^18 keV
Therefore, the final expression for the kinetic energy of 12 carbon atoms with a mass of 12.0 u and a speed of 2 x 10^6 m/s is:
KE = (1/2) * (1.992 x 10^-26 kg) * (4.4 keV)^2 * (6.242 x 10^18 keV/J)
Evaluating this expression will give you the kinetic energy of the 12 carbon atoms in kiloelectronvolt (keV).