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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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Why downvotes?? –  MyFavouritePhysicistIsNewtax Oct 19 '13 at 18:58
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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
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closed as unclear what you're asking by John Rennie, akhmeteli, David Z Oct 20 '13 at 20:22

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

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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
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To put the numbers in perspective: the sun roughly outputs $10^{45}$ photons per second (estimated here). –  Alexander Oct 19 '13 at 20:24
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@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
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