= Solution
Approximate <helium> <mass> by $2m_p+2m_n\simeq6.69\times10^{-27}$ kg. Nonrelativistic <momentum> is $p=\sqrt{2mT}$, giving $\boxed{\lambda=h/p\simeq0.203\ \mathrm{nm}}$. A transverse width of one micrometre implies a characteristic <position uncertainty> of that order and a minimum <momentum> uncertainty of order $\hbar/a\sim10^{-28}$ kg m s$^{-1}$, with factors depending on profile convention. For a uniform interval $\Delta x=a/\sqrt{12}$, but an exactly abrupt rectangular <wavefunction> actually has infinite rms <momentum> spread. Width alone does not uniquely specify both rms uncertainties; a smooth near-minimum-uncertainty beam is needed for a finite order-of-magnitude estimate.
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