There is also an uncertainty principle for energy and time d

There is also an uncertainty principle for energy and time: delta E delta t h Show that both sides of this expression have the same units. The relationship introduced in Problem 1 -48 has been interpreted to mean that a particle of mass m (E = mc^2) can materialize from nothing provided that it returns to nothing within a time delta t h / mc^2. Particles that last for time delta t or more are called real particles; particles that last less than time delta t are called virtual particles. The mass of the charged pion, a subatomic particle, is 2.5 x 10^-28 kg. What is the minimum lifetime if the pion is to be considered a real particle

Solution

Problem 1.48:

Uncertainty principle for energy and time: E*t h -----> Eqn. (1)

Dimension of energy is electron volts (eV)

Dimension of time is second (s)

Now,

Planck\'s constant (h) = 6.62607 * 10^-34 J-s

1 eV = 1.60218 * 10^-19 J

Hence, h = 4.13567 * 10^-15 eV-s

Thus, dimension of Planck\'s constant is product of electron volt (dimension of energy) and second (dimension of time)

Therefore, in Eqn.(1) both sides have same units.

Problem 1.49:

For considering pion to be a real particle, expected life time is t = h/(mc²), where m is the mass of the pion and c is velocity of light, i.e., 3*10⁸ m/s

Mass of pion = m = 2.5 * 10^-28 kg

Using above values, mc² = 22.5* 10^-12 kg-m²/s² = 22.5* 10^-12 J

Thus, t = 2.94492 * 10^-23 s