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An antenna pointing in a certain direction has a noise temperature of $50 \: K$. The ambient temperature is $290 \: K$. The antenna is connected to a pre-amplifier that has a noise figure of $2$ dB and an available gain of $40$ dB over an effective bandwidth of $12$ MHz. The effective input noise temperature $T_e$ for the amplifier and the noise power $P_{a0}$ at the output of the preamplifier, respectively, are

1. $T_e = 169.36\thinspace K$ and $P_{a0} = 3.73 \times10^{-10}W$
2. $T_e = 170.8\thinspace K$   and $P_{a0} = 4.56 \times 10^{-10}W$
3. $T_e = 182.5\thinspace K$   and $P_{a0} = 3.85 \times 10^{-10}W$
4. $T_e = 160.62\thinspace K$ and $P_{a0} = 4.6\times 10^{-10}W$