Energy of a photon absorbed by an elementary particle

[saridy]

Homework Statement

An elementary particle of mass M completely absorbs a photon, after which its mass is 1.01M.
a) What was the energy of the incoming photon?
b) Why is that energy greater than 0.01Mc²?

Homework Equations

E = mc² or Δm = Δ E/c²
E = γmc²

The Attempt at a Solution

The only thing I can see doing is Δm = 1.01M - M = 0.01M = E/c²
But that gives E = 0.01Mc² , which according to part b is not the answer. How do you solve this?

 

[saridy]

After further reading, I'll add these equations:
(mc²)² = E² - (pc)²
E = pc (for m = 0)

 

[saridy]

OKAY. so I got an answer of 0.01005Mc^2, so I'd appreciate if someone could check/correct that for me. I still don't know how to explain it in part b.