Respuesta :
Answer:
Velocity will be [tex]v=4.06\times10^7m/sec[/tex]
Explanation:
We have given mass of alpha particle m = 4 u [tex]=4\times 1.67\times 10^{-27}kg=6.68\times 10^{-27}kg[/tex]
Charge on alpha particle [tex]q=2e=2\times 1.6\times 10^{-19}C=3.2\times 10^{-19}C[/tex]
Charge on thorium particle [tex]=90\times 1.6\times 10^{-19}=144\times 10^{-19}C[/tex]
Diameter is given as d = 15 fm
So radius [tex]r=\frac{d}{2}=\frac{15}{2}=7.5fm=7.5\times 10^{-15}m[/tex]
Potential energy is given by [tex]E=\frac{1}{4\pi \epsilon _0}\frac{q_1q_2}{r}=\frac{Kq_1q_2}{r}=\frac{9\times 10^9\times 144\times 10^{-19}\times 3.2\times 10^{-19}}{7.5\times 10^{-15}}=5.529\times 10^{-12}J[/tex]
From energy conservation [tex]\frac{1}{2}mv^2=5.529\times 10^{-12}[/tex]
[tex]\frac{1}{2}\times 6.68\times 10^{-27}v^2=5.529\times 10^{-12}[/tex]
[tex]v=4.06\times10^7m/sec[/tex]
Speed is a ratio of distance and time. The speed of the alpha particle when it is detected in the laboratory is 4.06 x 10⁷ m/s
What is speed?
Speed is the ratio of distance and time. It tells us how fast an object is moving with respect to time.
[tex]\rm Speed=\dfrac{Distance}{Time}[/tex]
Given to us
Mass of the alpha particel, m = 4u = 6.68 x 10⁻²⁷ kg
Charge of the alpha particle, q = 2e = 3.2 x 10⁻¹⁹ C
Charge of the thorium particle, Q = 90e = 144 x 10⁻¹⁹ C
Diameter of the thorium, d = 15 fm = 15 x 10⁻¹⁵ m
Radius of the thorium, r = 7.5 fm = 7.5 x 10⁻¹⁵ m
We know that the potential energy of any particle is given as,
[tex]PE = E = k\dfrac{q_1q_2}{R}[/tex]
Substitute the values,
[tex]E = 9.8 \times 10^9 \times \dfrac{144 \times 10^{-19}\times 3.2 \times 10^{-19}}{7.5 4 \times 10^{-15}}[/tex]
E = 5.529 x 10⁻¹² J
We know that according to the law of conservation of energy,
[tex]\rm Kinetic\ Energy = Potential\ energy[/tex]
[tex]\dfrac{1}{2} m v^2 = 5.529 \times 10^{-12}\\\\v = 4.06 \times 10^7\ m/s[/tex]
Hence, the speed of the alpha particle when it is detected in the laboratory is 4.06 x 10⁷ m/s.
Learn more about Speed:
https://brainly.com/question/7359669
