Question

An atom is restricted to move in one dimension by making unit jumps either to the left or right, as shown in the figure. Assuming that a jump to the left or right is equally probable, the probability of the atom returning back to the starting point after four jumps is Atom -4 -3 -2 -1 0 1 2 3 (A) 0.250 (B) 0.333 (C) 0.375 (D) 0.500

The correct answer is option (c) 0.375

Answer 1

Atom restricted to move in one dimerion by making unit jumps. either to left or to the righte both Left and right of chit Juupe. are equally probable. Atom + -3 + + -2 o 2 3 probability of Unit probability of 4 successive Unit Jump 2 Jumps 22 Would be Ž P (4 Jelups) > P (4 Jelups) = 1 x L xlx P (4 Jumps) = 6)=# Now. for atom to return to its original poser After 4 successive Temps. let's see number of possibilities. 16

7 + -4 -3 -2 -1 + 4 0 2 3 of o to to - In schots 6 2 possibilities. 3 t -4 -3 3941 ol -2 - 1 О 2 3 4 Otol - I to 2 _ oto-1 -1 to In 4 Steps ㅌ total 2 bessibilities, 2 o -3 -2 + 3 2 4 o to I ootto le of o 4 steps I to o some for both ways » total 2 possibilities

Here 3 cases are possible with 2 possibilities each. In total 6 possibilities. probability Atoom Returning bark to Initial posn After 4 Jumpe P (4 unit Jumps) x 6 txt = 16 = 0.375 option (C) ) 0.375 v correct