The average lifetime ofa pi meson in its own frame of reference (i.e., the prope

Question

The average lifetime ofa pi meson in its own frame of reference (i.e., the properlifetime) is 2.6 × 10–8s. If the meson moves with a speed of0.98c, what is:

(a) its mean lifetime as measured by an observer on Earth and

(b) the average distance it travels before decaying as measured byan observer on Earth?

(c) What distance would it travel if time dilation did notoccur? The average lifetime ofa pi meson in its own frame of reference (i.e., the properlifetime) is 2.6 × 10–8s. If the meson moves with a speed of0.98c, what is:

(a) its mean lifetime as measured by an observer on Earth and

(b) the average distance it travels before decaying as measured byan observer on Earth?

(c) What distance would it travel if time dilation did notoccur?

Explanation / Answer

   a.   Time is dilated as perrelation   t   =   t0/ (1 - v2/c2)          timeobserved atearth   t   =   2.6 *10-8 / (1 - (0.98 * c /c)2)   =   13.06 *10-8   s    b.   distancecovered   d   =   v *t   =   0.98 * 3 * 108 *13.06 *10-8   =   38.40   m    c.   d0   =   v* t0   =   0.98 * 3 *108 * 2.6 *10-8   =   7.64   m

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