Question

alpha particle and proton head directly towards each other at an initial speed of 0.003c what is their distance of closest approach

Answer 1

Alpha particle  ( q=+2e, m =4u) and proton head directly towards each other at an initial speed of 0.003c their distance of closest approach is  1.5 × 10⁻¹⁴ m

The charge on the proton = e

the charge on the alpha particle = 2e

mass of proton = mp = 1.67 × 10⁻²⁷ kg

mass of alpha particle = ma = 4mp = 6.68 × 10⁻²⁷ kg

the distance is given as :

r = (k2e² ( mp + ma) )/ 2 ma mp vp²

r = (9 × 10⁹ × 2 ( 1.67 × 10⁻²⁷ )² (  1.67 × 10⁻²⁷  + 6.68 × 10⁻²⁷) ) / ( 2(6.68 ×  

                                                       10⁻²⁷ × 1.67 × 10⁻²⁷ (0.003 × 3 × 10⁸)²

r = 1.5 × 10⁻¹⁴ m

Thus, Alpha particle and proton head directly towards each other at an initial speed of 0.003c their distance of closest approach is  1.5 × 10⁻¹⁴ m

To learn more about alpha particle here

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