Plank time t p , the value of which depends on three fundamental constants: (1)
ID: 2113692 • Letter: P
Question
Plank time tp, the value of which depends on three fundamental constants:
(1) the speed of light (the fundamental constant of relativity), c= 3x108 m/s;
(2) Newton%u2019s gravitational constant (the fundamental constant of gravity),
G =6.67x10-11 m3/s2.kg; and (3) Plank%u2019s constant (the fundamental constant of
quantum mechanics), h=6.63x10-34 kg.m2/s. Based on a dimensional analysis,
find the value of the Plank time.
Answer: tp = 1.35 x 10-43 s
Can you find Plank length, and Plank mass?
Please show all work and steps! thanks!
Explanation / Answer
tp = [T]
c = [LT^-1]
G = [M^-1L^3T^-2]
h = [ML^2T^-1]
Comparing we get ,
tp = sqrt( h*G/c^5)
Putting the values we get
tp = 1.35 x 10^-43 s
plank length(lp) depends on h, G and c
Comparing we get,
lp = sqrt( h*G/c^3) = 1.616 x 10^-35 m
planck mass(mp) = sqrt(h*c/G) = 2.176 x 10^-8 kg