Q)1 : Alpha particles travel through a magnetic field of 0.360T and are deflected in an arc of 0.0820m. Assuming the alpha particle are perpendicular to the field, what is the energy of an individual alpha particle?
do i use the value of q/m ratio??
and thank u =)
Magnetic field B = 0.36 T
Deflected radius of an arc r = 0.082 m
Charge of alpha particle q = 2e = 3.20435 × 10^-19 C
Mass of alpha particle m = 6.64 × 10^−27 kg
Magnetic Force = Bqv
Centripetal Force = mv²/r
Bqv = mv²/r
v = Bqr/m
v = (0.36)( 3.20435 × 10^-19)( 0.082) / (6.64 × 10^−27)
v = 1.42458 × 10^6 m/s
Energy of alpha particle E = (1/2)mv²
E = (1/2)( 6.64 × 10−27)( 1.42458 × 106)²
E = 4.7296 × 10^−15 J
Energy of alpha particle is 4.7296 × 10^−15 J.
calculate the velocity:
Bqv=Force
and force= massalpha*v^2/r
bqv=massv^2/r
solve for v.
A) Well, if we're talking about alpha particles, we might as well call them the "superheroes" of the particle world. With their ability to pierce through materials, they're like the Superman of subatomic particles! Now, let's get down to business.
To find the energy of an individual alpha particle, we can use the formula: E = Bqv, where E is the energy, B is the magnetic field, q is the charge of the particle, and v is the velocity.
Since we know the magnetic field (B = 0.360 T) and the particle is perpendicular to the field, we can say that the angle between the velocity of the particle and the magnetic field is 90 degrees. This means that the sine of 90 degrees is equal to 1.
To find the velocity of the particle, we can use the formula: v = s/t, where v is the velocity, s is the arc length, and t is the time taken to travel that distance.
Now, you've given me an arc length of 0.0820 m, but unfortunately, I don't have the time information. I guess this alpha particle has gone incognito and is refusing to share its travel time. I hear they're quite secretive!
Without the time information, I'm afraid I can't calculate the velocity, and without the velocity, I can't calculate the energy of the alpha particle. It looks like this alpha particle is playing hard to get. Maybe it wants to keep its energy a secret!
To find the energy of an individual alpha particle, we can use the equation that relates the energy and the magnetic field in a circular motion:
E = BqRv
Where:
E = energy of the particle
B = magnetic field strength
q = charge of the particle
R = radius of the circular path
v = velocity of the particle
Given:
B = 0.360 T
R = 0.0820 m
q = 2e (alpha particles have a charge of +2e, where e is the elementary charge)
Now we need to find the velocity of the particle. We know that the path of the particle is a circular arc, so we can use the equation for the circumference of a circle to find the distance traveled:
C = 2πR
Rearranging the equation, we can solve for v:
v = C / T
Where:
C = circumference of the circular path
T = time taken to complete the circular path
Since no time is given in the problem, we cannot directly calculate the velocity. However, we know that the alpha particles are deflected in an arc, which means they move in a circular path. Therefore, we can assume that the entire arc corresponds to a half-circle.
Therefore, the circumference of the circular path is equal to the distance traveled by the alpha particle, which is 0.0820 m.
Plugging in the values into the equation for velocity:
v = 0.0820 m / (0.5T)
Now, we can substitute the values of B, q, R, and v into the equation for energy:
E = (0.360 T) * (2e) * (0.0820 m) * [0.0820 m / (0.5T)]
Simplifying the equation:
E = 0.360 T * 2 * (0.0820 m)² / T
Canceling out the T:
E = 0.360 T * 2 * (0.0820 m)²
E = 0.118 T * m²
Therefore, the energy of an individual alpha particle using these given values is 0.118 T * m².