How much photons are needed to erase a complete mountain? [closed]

I've heard that light does change our momentum a little bit which made me think: How much photons are needed to erase a complete mountain? That is to evaporate a complete mountain such as Himalaya for instance.

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closed as unclear what you're asking by John Rennie, akhmeteli, David Z♦Oct 20 '13 at 20:22

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Why downvotes?? –  MyFavouritePhysicistIsNewtax Oct 19 '13 at 18:58
Your question doesn't really make sense. What do you mean by "erase a mountain"? It's not clear what the physics content in this is supposed to be. –  David Z Oct 19 '13 at 22:29

Let's say Himalaya is $8\text{ km}$ high, $50\text{ km}$ wide and $2400\text{ km}$ long. Let's assume it is mainly made of granite. Then it's volume is: $$\frac{8 \cdot 50\cdot 2400}{2} = 480000\text{ km}^3 = 4.8 \cdot 10^5 \text{ km}^3$$ The mass of $1\text{ km}^3$ of granite is $2.7\cdot10^{12}\text{ kg}$. So total mass is $1.296\cdot10^{17}\text{ kg}$.

Let's assume that granite heat capacity is almost the same as for $\text{SiO2}$, so $733 \text{ J/Kg}$. It's boiling temperature is $2230\text{ C}$, so we need $~1634590 J*kg = 1.6*10^6 J*kg$. Let's skip phase change energy expenses, they are not too big compared to this figure.

So you need 2,0736*10^23 Joules of energy. That's about 500'000 1Mt nuclear bombs.

Last part, how many photons is needed? Let's assume we'll use 532nm green photons.

1 such photon has energy of 3.734*10-19 Joule. So required number of photons is: 2,0736*10^23/3.734*10-19 = 5,55 * 10^41. Quite a bit of photons.

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5.55 * 10e-41 photons per sec? –  MyFavouritePhysicistIsNewtax Oct 19 '13 at 19:48
To put the numbers in perspective: the sun roughly outputs $10^{45}$ photons per second (estimated here). –  Alexander Oct 19 '13 at 20:24
@MyFavouritePhysicistIsNewtax That's total, not per sec. But if you do this too slow - heat will just dissipate :-) –  BarsMonster Oct 19 '13 at 21:26
Won't work for SiO2 with 532 nm. SiO2 has very low absorption of light with 532 nm. 430 nm is a better choice. –  user1800 Oct 21 '13 at 17:22
@user1800 You are correct about pure SiO2, though granite is not transparent :-) –  BarsMonster Oct 21 '13 at 20:37