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m refers to the mass of the object you are calculating. In some problems, the mass is not always an atom; it could be a baseball or car. However those values usually give wavelengths that are undetectable. m can also refer to the mass of an electron or neutron.
The "m" in De Broglie's equation refers to the mass of the object with momentum, P, and has wavelike properties with wavelength. However if the mass is large then the object most likely does not have detectable wave-light property and acts more like a particle.
m could represent the mass of an object, like a baseball or car as others mentioned, or a particle such as a proton, neutron, or electron. The only thing it can't represent is a photon since photons have no mass. If the problem involves a photon/light, use c=wavelength*frequency.
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