Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal
The resolution in the DFT is given by: $ \frac{{F}_{s}}{N} $.
Hence you need 10e6 / 100 = 100,000 samples to get the resolution you want.
You may bring the signal to the baseband (demodulation) and then you'll need a lower frequency of sampling to achieve what you want.
Since the effective bandwidth of the signal is (Two Sided) 50 [KHz], it can be sampled at $ {F}_{S} = 50 [KHz] $ and only 500 samples would be required for the asked resolution.