Large language models (LLMs) can store a massive amount of knowledge, yet their potential to acquire new knowledge remains unknown. We propose a novel evaluation framework that evaluates this capability. This framework prompts LLMs to generate questions about a statement introducing scientific knowledge, simulating a curious person when facing the statement for the first time. We score the qualities of the generated questions, thereby evaluating the knowledge acquisition potential of the LLM. We apply controlled ablation studies to validate our scoring procedures. Additionally, we created a synthetic dataset consisting of 1101 statements in physics, chemistry, and maths with distinct levels of difficulties, 300 general knowledge statements, and 567 incorrect statements. Human evaluations were conducted to validate our model assessments, achieving an approximate weighted Cohen's kappa of 0.7 on all three metrics considered. We find that while large models like GPT-4 and Mistral 8x7b are adept at generating coherent and relevant questions, the smaller Phi-2 model is equally or more effective. This indicates that size does not solely determine a model's knowledge acquisition potential. The proposed framework quantifies a critical model capability that was commonly overlooked and opens up research opportunities for developing more knowledgeable AI systems