Answer
a) $ 2.43\times 10^5\;\rm Pa$
b) $352\;\rm K$
Work Step by Step
a)
Now we can find the temperature which is given by
$$PV=Nk_BT$$
We know that the rms speed is given by
$$v_{rms}=\sqrt{\dfrac{3k_BT}{m}}$$
Hence,
$$T=\dfrac{mv_{rms}^2 }{3k_B}=\dfrac{(3.35\times 10^{-26})(660)^2}{3(1.38\times 10^{-23})}$$
$$T=\color{red}{\bf 352}\;\rm K$$
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b)
We know that pressure is given by
$$P=\left(\dfrac{N}{V}\right)\dfrac{mv_{\rm rms}^2}{3}$$
So to find the pressure, we need to find the mass of the neon atom.
$$m_{Ne}=20.2\;\rm u=20.2\times 1.66\times 10^{-27}$$
Hence,
$$m_{Ne}=\bf 3.35\times 10^{-26}\;\rm kg$$
Plugging the known;
$$P=\left({5.00\times 10^{25}}\right)\dfrac{(3.35\times 10^{-26})(660)^2}{3}$$
$$P=\color{red}{\bf 2.43\times 10^5}\;\rm Pa$$
