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That would depend on:

  • Size of mountain
  • Type of rock in mountain
  • Yield of bomb
  • Depth of burst in mountain (an air burst would have little effect on any mountain) This means either a placed charge or a rock penetrator bomb

My Nuclear Bomb Effects Computer circular slide rule computes that for a 20 Mton bomb surface burst (the slide rule is not calibrated beyond 20 Mtons and does not include underground bursts) results in a crater 660 feet deep and 2534 feet in diameter. The depth and diameter of the crater will increase with depth of burst, until a depth (depending on yield) at which the rock begins to contain the blast.

Extrapolating and decalibrating the slide rule for a 200 Mton bomb surface burst results in a crater 1,320 feet deep and 5,700 feet in diameter.

Much larger than this yield and most of the blast, even in a surface burst will simply blow away atmosphere above the burst into space.

Yes, a high enough yield device (there is no theoretical limit to the yield of a fusion bomb) at the right depth candestroy a mountain. However I would hate to be anywhere downwind as every speck of the mountain will come falling back as highly radioactive fallout.

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