0.6764*10^-10m
Explanation:
Using E= hc/wavelength
(4.14x10^-15)x(3.0x10^8)/(65x10^-12)=0.1911x10^5 eV=19.1 keV
So subtract the calculated energy from the given energy of scattered photons
9.11-0.75=18.36 keV
To find wavelength
Wavelength= hc/ E
[(4.14x 10^-15)x (3.0x10^8)]/(18.36*10^3) =0.6764^-10 m
To find the temperature it is necessary to use the expression and concepts related to the ideal gas law.
Mathematically it can be defined as

Where
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
When the number of moles and volume is constant then the expression can be written as

Or in practical terms for this exercise depending on the final temperature:

Our values are given as

Replacing

Therefore the final temperature of the gas is 800K